Because this unit is a "used trans", some interesting intangibles come into play.
Questions like, how did it work before you installed it into your vehicle, what was the fluid condition, are there any valves in the valve body, such as mtv up or tv valve itself sticking, which will create this problem.
Most early upshifts, in a known good working transmission, will be because of incorrect tv cable adjustment.
When adjusting the cable makes no difference in the upshift pattern one starts to consider if one may have a control issue with the unit, such as sticking valves.
Your tv cable geometry is more than likely a concern, as well, which can also add to your problem, if in fact not be the cause of the problem.
There is a link on this site that explains not only the importance of this geometry, but how to correct it as well.