Is this normal, or a problem?

[PSU 98]

From a stoplight today, car in "D", I got on it up a hill. RPMs climbed to around 6000 and I saw red on the tach. Instead of shifting to "OD" I just got out of throttle and let the RPMs drop but I don't think the car ever downshifted. Will the GN stay in 3rd all the way to redline under heavy throttle, or should it have shifted into 4th on its own? I know this trans was rebuilt at some point by the P.O., and a cooler was already installed.

 

[hiboom]

shift

If you looking at the tach in the dash they are not real accurate unless you have had it fixed my car will not shift out of drive if the gear selector is in D unless I manually shift it into overdrive

 

[PSU 98]

It was really the sound of the engine that made me look at the RPMs. I've never had an auto trans hang at redline like that before.