Why does the 1991 Dodge Stealth jerks in every gear unless excelerating and then it runs smooth and could the timing belt tension cause this problem?

No the Timing Belt has Nothing to do with the Transmission. When was the last service you had done on the Transmission. Regular Service Keeps Your Transmission on the Road…
Servicing your car’s automatic transmission regularly can dramatically extend its life. That’s because the oil — or ATF — does more than just lubricate: It also helps drive the transmission. Damage to the fluid, such as oxidation and shear, will reduce its holding power. This allows the transmission to slip and overheat, and quickly cause it to fail. A complete fluid exchange service, performed annually, can add years to your transmission’s life. For Example GMC say's this about Automatic Transmission Fluid and Filter Replacement Interval:
Every 100000 miles unless the vehicle is mainly driven under one or more of these conditions:
1) In heavy city traffic where the outside temperature regularly reaches 90 F (32 C) or higher.
2) In hilly or mountainous terrain.
3) When doing frequent trailering. Good Luck and Remember.
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No the Timing Belt has Nothing to do with the Transmission. When was the last service you had done on the Transmission. Regular Service Keeps Your Transmission on the Road