Swap is 1 to 1, so this can be used both to get TP to yourself as well as to the automaton. This can potentially allow you or the automaton to solo skill chain.
Recommendation is to use a macro like <pettp> to see the Automaton's TP, so you can plan a skill chain. If you want to use two Weapon Skills on your own, use Retrieve so the automaton doesn't use its TP. If you want the automaton to do it, simply wait for it to use its TP and switch.
Consecutive TP swaps can increase TP above 300, but any action (attack, being hit, etc) that gains TP will reset the value back to 300. Weaponskills with 300+TP will still cap at 300TP (and thus waste the remainder), but TP consuming abilities such as /DNC Curing Waltz will only use what is needed and leave any remaining TP over 300.
This ability can also be enhanced through the "Tactical Switch" Job Point category. Any additional TP granted through the job point category is added in after calculating in the additional TP granted by the Cirque or Karagoz Scarpe.