Effect on video with mask

Or pre-compose after applying time warp and add a mask,

Or copy the mask path, create a anew shape layer by clicking anywhere with the pen tool and then paste and use the shape layer as the source for Effect>Channel>Set Matte,

Or put the shape layer or a mask at the bottom of your composition and enable preserve underlying transparency modes column,

Or put your shape layer or mask layer at the above the time warped video and select Stencil Alpha from the Modes column,

Or .....

You get the idea? There are a bunch of ways to fix the rendering pipeline problem caused by many effects like Time Warp. The best and most efficient way to do it depends entirely on what else is going on in your composition. For the most efficient and fastest rendering option we need workflow details including exactly what you are trying to accomplish and a full app screenshot with the modified properties of all layers in question revealed (press uu) so we can point you in the right direction. Most likely a track matte or stencil alpha option using a copy of the mask will be the most efficient --- but you never know.