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This would depend on how those pieces are defined. If they are treated as making two separate moves on the same turn, and the second move is capable of checking the King, things could prove difficult. If their move is treated as a single move that requires a turning point, or checking is allowed only on the first part of a move, then it's not a problem. There could even be a hybrid solution, in which the piece has a checking-only move that completes the whole move, but it otherwise handles actual moves as a pair of separate moves.

With regard to Sissa, perhaps the hybrid solution is the right one. Take into account the uniqueness of this piece. In the diagram below the blue King is in check in two different ways but what is somewhat paradoxical is that by moving to d6 or e6 it evades the check.