About 10 years ago, I put down self-adhesive vinyl tile over the dated and heavily-stained linoleum in the 3rd floor kitchen. Before I installed the tile, I washed the floor thoroughly, and then used a degreaser to get rid of any contaminants that might've been on the floor. It seems like about a year or so after installing them, the tiles started to shift in front of the sink and other high traffic areas. This was especially noticeable in the summer. If you leaned against the counter, the tile under your feet would shift a bit.

I've installed self-adhesive vinyl over ancient (like 60+ years or so) linoleum and never had any sort of issue (aside from the surface finish wearing a bit), but then again, that wasn't a rental property.

Now, I want to pull up this tile and start fresh with brand name tiles like Armstrong, etc. Can I leave the old linoleum down on the floor? The kitchen has two moveable skylights and I wonder if the linoleum would help contain any water that (God Forbid) might ever come in due to tenant negligence or otherwise. Would the linoleum provide any sort of barrier to moister?

I've never used any sort of floor adhesive on these types of tiles; I've just relied on the adhesive on the back of each tile... Should I be using products like these in addition to the adhesive already on the tile?