How about a picture of the rack?
(or link to mfr site )

Is the tile install "old school", set in a heavy concrete mortar bed or
just glued to the paper on green board?

I'd drill (rotary hammer) a 1/4" diameter hole into the back of the
rack.

then I'd either

1) set a 1/4" stud in the tile / mortar w/ epoxy (SIKA AnchorFix fast
set)

2) use a toggle & jam nut to set a sud in the wall

With a stud now protruding from the wall, I'd AnchorFix the drilled
rack base to the stud.

Use the fast set AnchorFix & it's gelled hard in ~5 minutes & fully
cured in ~1hr @70F

adhesive alone would make me nervous unless this thing it to small to
damaged the floor or someone's foot when it falls. I've had too many
adhesive only face bonds fail.

Silicone seal MIGHT work if allowed to cured un-weighted for about a
week but it would depend on the size of the base relative to rack
wieght & payload..

AnchorFix alone would glue the rack base to the tile but will the tile
hold to the wall?

Plus "belt & suspenders" is always good, consider the cost of failure.

cheers
Bob