I've noticed this problem both with the antimatter recharger and the Vasari nano weapons jammer. Their autocast condiitons are messed up for some reason. If you playing single player you can mod these away, but you are right it is very annoying. Though just to clarify, it will still restore antimatter for your units, it just won't do so as fast as it would if it had full antimatter.

No, it should restore antimatter to your other structures too. The only other structures I can think of that have antitmatter though are hangars, repair bays and starbases though.

It is a bug (already reported) where the antimatter recharger continuously casts over and over again.  This bug will be fixed in the next patch of the game.

For now, you can work around the problem by TURNING OFF AUTOCAST for the antimatter recharger.  Then it will not autocast over and over again and waste all its antimatter.  To use it, simply manually cast it yourself.

It is a useful ability, unique to Advent.  By all means build and use the structure.  Turn off autocast, and wait for the next patch of the game which should fix the problem.

no, checked the coding, it only targets capital ships and frigates with antimatter

Nope, but I may have also not been paying close attnetion. That seems worthless then, or not as worthwhile.

A good advent player should have better culture than a TEC player though (because if is more important for the advent economy), so it only really helps in defensive situations. And rechargers are effective if you have a couple of high level capital ships near them (and that was before starbases). Also, I like to get a Revelation to level 5 to get level 3 clairvoyance and park it by an antimatter recharger. Makes it hard for the enemy to hide much from you with that ability going off at max speed, without reguard for antimatter (though just placing it in a star can be just as effective).