Toilet off a shower pump
 

I'm just about to move into a new build and I got a shower pump to run
the upstairs power shower and taps for better performance. However I'm
just after noticing that the plumber has used the same cold water feed
from the pump to run to the toilet cisterns. Consequently whenever the
loos upstairs are flushed the pump comes on, and on one of the toilets,
the refill is slow and the pumps goes chugga chugga for a few minutes
before the cistern fills up again i.e. low flow rate not opening pump
valve fully.

Should the plumber have used a seperate feed to the cisterns and if so
should I insist he sorts it out before we move in? Could the slow
refill on the problem cistern be adjusted so that it fills more quickly?