I’m thinking something along this:
The layer above the tiles (the control layer) will be an animation with an alpha mask,
and whenever, for example, a black pixel is over a tile in the layer below,
it triggers the short video clip.
As for the rules for starting/ending a clip I would say ideally:
If a clip is triggered it plays through till the last frame,
and only then can it be triggered again by the control layer.
Thanks,
Eran.