Wall to wall won't hold them, because they expand and contract a significant amount with any temperature change. Before using double sided tape or construction adhesive, I would suggest using low pile carpet tiles under the mats. With this, the mats won't get damaged if they shift, and it is easier to pick them up and clean them or clean under them (like if something gets spilled on them).

Buy a few rolls of mat tape and use those to cover all the seams. You can go with clear, or get colored opaque "striping" mat tape if you want to have some sort of pattern to your edges and completely hide the seams. That will make the tiles shift as one big mat, reduce gaps, resist spills and dirt getting under the mats, and make anchoring the mats more effective.