Water can leak from the cap area duing a refill, that's part of the antisiphon, that's normal.
Water from the tube, that points into the overflow tube, that would be normal. That fills the bowl after a flush.
If, after everyything has filled, then things should go quiet.
There are two fill valves used on the Ultramax.
The Korky type, can be cleaned or repaired using these instructions
If you have the type, with the screw adjustment, and it does not come to a complete shutoff when finished, then you would be looking at replacement.
Looking inside the Ultimate tank, wth the Korky style fill valve.
And with the fill valve that has a screen at the bottom where the water comes in.