Kitty's passive reads "...if there are 4 or more friendly Strike, Attack, or Protect tiles on the board, improve them by...". However, I've noticed that sometimes her passive continues to activate with only 3 tiles. I say 'continues' because I've only ever noticed this occurring when Kitty has 4* Rocket & Groot as a teammate, and his "Welcome to the Team" passive creates at least 4 strike tiles at the start of battle. As long as she improves the tiles at least once, she will still continue to improve the tiles even if the total number dips down to 3.
The tile count requirement is decreased by one for each X-Man on her team.
I believe she counts herself in the "For every member of the X-Men on Kitty's team, this threshold goes down by 1." bit at the end. Not entirely sure, but I think so.
3 Strike Tiles of strength 415 equal 1245.
Kitty strengthens each tile by 138.
3 Strike Tiles of strength 553 equal 1659.
Psylocke is a member of the X-Men, so Kitty only needs to have 3 tiles to meet the threshold for strengthening them.