You don't need to have Tetryon weapons to use Tetryon Glider. It just adds extra damage to shields.
However, you do need to have polaron weapons to use the Jem H'dar set.
Indeed. Tetryon Glider averages 9x faster shield drain than the base tetryon weapon proc, so base tetryon weapons are inefficient anti-shield weapons when compared to Tetryon Glider.
The Jem'Hadar set has a number of deficiencies:
1) the lowest capacity, slowest recharge purple set shield
2) combat impulse engines = can't chase very well due to low top speed
3) nominal 7.5% weapon bonus (tactical consoles have +26%), and only for polarons
4) Dominion Synergy buff-removal's low 1% proc trigger rate, and only in Galors and JHAS.
In short, unless you have a Galor or JHAS, you're better off using almost any other set depending on your build (other than the Breen set, which is arguably the weakest set presently in the game).