When running seismic and grillage analyses the program pops up a tie-in query. Does it mean, an affirmative in the grillage analysis will cause the program adding the earthquake-induced sloshing pressure to the equation?

No. The "Grillage" and "Seismic" input dialogs share two common data items; bottom plate thickness, and minimum yield strength of bottom plate. When you specify either of these items, in either dialog, the program pops up a prompt asking if you want the entered value to change the same item on "the other dialog". This is so that you don't (accidentally) have two different values for the bottom plate thickness, or minimum yield strength of bottom plate.

Note, the program doesn't prevent you from having different values for these items, its just that without the pop-up it would be easy to do accidentally.