I think the bottom line here is that you put the tape over the caulk before it was dry enough.

Acrylic latex caulks don't have a chemical curing process like polyurethane caulks or oil based paints. Instead, they undergo a physical transformation as they "dry", exactly like acrylic latex paints do as they "dry".

I'll explain the physical transformation that occurs in latex paints, and exactly the same thing happens in acrylic caulks, but with different solvents and different resins:

A latex paint consists of a slurry of solids suspended in a liquid.

The solids consist of:
1. Hard transparent and colourless plastic resins made of one of two kinds of plastic
2. coarse solids called "extender pigments" that cause the paint to dry to a rougher finish. Were it not for extender pigments, all paints would dry to a high gloss finish.
e. fine solid particles called "coloured pigments" that give the paint it's colour.

The liquid those solids are suspended in consists of:
A. water, and
B. a low volatility water soluble solvent called a "coalescing agent" or "coalescing solvent". Probably the most commonly used coalescing solvent is a product called "Texanol" made by the Eastman Chemical Company.

http://www.eastman.com/literature_center/m/m329.pdf

C. glycerine, which is added with the colourants called for in the tint formula when the paint is tinted at the point of sale.

When the paint is applied to a wall or ceiling, the first thing that happens is the water starts to evaporate. As the water evaporates, each of the hard spherical plastic resins finds itself in a bath of coalescing solvent at steadily increasing concentration. The coalescing solvent gets absorbed into the hard clear spherical plastic resins causing them to become very soft and sticky.

The forces of surface tension and capillary pressure which cause tiny droplets of water to coalesce into large heavy rain drops then take over to cause each soft sticky plastic resin to stick to and pull on each of it's neighbors. As that happens, there is a rapid reduction in the number of liquid/plastic interfaces which reflect and refract light to produce the colour white in an observers eyes, and the paint film darkens slightly as a result.

In proper film formation, all of the soft sticky plastic resins pull on each other with sufficient force to eliminate the phase boundaries around each resin, and the result is a solid soft sticky film of clear plastic with the extender and coloured pigments suspended in it very much like raisins in raisin bread.

Then, over the next 12 to 48 hours, the coalescing solvent evaporates from the paint film filling the room with that "freshly painted smell". You can create that freshly painted smell in any room simply by using a spray bottle to mist some Texanol into the air.

As the coalescing solvent evaporates from the paint film, the plastic hardens up again to the same hardness the plastic resins originally were in the liquid paint before the can was opened. Only, instead of being microscopically small spheres of plastic, they now consists of a continuous solid film of plastic with pigments suspended inside it.

The above explains why latex paints darken as they dry. Initially, there is reflection and refraction of light at every plastic/liquid interface, and so latex paint is white for the same reason that clowds and snow is white. Your eye sees all the different colours of refracted and reflected light coming from everywhere in the paint film as the colour "white". As the plastic resins coalesce into a solid film, there is a rapid reduction in the amount of reflection and refraction of light within the paint film, and the paint darkens in very much the same way that snow loses it's white colour as it melts to form water.

Also, over tinting the paint with too much colourant can ruin latex paints. The reason for this is that the coalescence process requires that the concentration of coalescing solvent in the plastic resins become high enough to fully soften the resins so that they deform easily to form a solid continuous film with no voids in it. If there was too much glycerine added when tinting the paint, that will dilute the concentration of coalescing solvent in the wet paint film after the water evaporates. The concentration of coalescing solvents might not be high enough to soften the plastic resins sufficiently that they deform easily enough to form a solid continuous film.

And finally, painting with a latex paint in cold temperatures can be problematic because every plastic gets harder when it's cold, and the cold temperature can make the clear plastic resins too hard to soften sufficiently from the absorbtion of coalescing solvents alone. That's why you're not supposed to paint when the outdoor temperature will fall below 50 deg. F at night.

What very well may have happened is that by pushing the tape on the "dry to the touch" caulk, you prevented the remaining coalescing solvent in the caulk from evaporating normally from the caulk. The result would be that the plastic resins at the surface of the caulk would have turned softer and stickier as they absorbed coalescing solvent for a second time. If you pushed the painter's tape onto those sticky resins, they would have stuck to the adhesive on the tape, and your now pulling that tape off is taking chunks of acrylic caulk with it.

I don't see any way around this problem. The resins are sticking to the tape adhesive just as they would wood or glass. I'd say your best bet it to just pull the tape off, and paint over the caulk so that it sheds water easily. I'm concerned that if you leave the caulk rough, then water will collect on it and mold will start growing in those collection points. Better to paint over the caulk so that the water drains off the paint surface after a rain.

Next time, allow more time for the caulk to dry before applying the painter's masking tape.