When I am driving, pop it into neutral and then back into drive when the car is in 4th gear....the engine rpms go way up and the car jerks forward, as I suppose it shifts down to 3rd before going back up into 4th...

It happens at any speed as long as its in 4th.

Is this supposed to happen? Or should it go right back to 4th out of neutral?

Thanks

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2016 Monsoon Gray Audi Allroad - 21k
2008 Black Mercedes E350 4Matic Sport - 131k
2014 Jeep Wranger Unlimited Sahara - 62k
2003 Gray Mercedes ML350 - 122k

Why would you do something that makes no sense, and will possibly damage the trans.
I believe that trans still has a forward pump which in the old days allowed an automatic to be push started.

A few nights a month I go to the gym late at night and its downhill all the way so I just put it in neutral and cruise. Is that really bad for the transmission with the engine still running?

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2016 Monsoon Gray Audi Allroad - 21k
2008 Black Mercedes E350 4Matic Sport - 131k
2014 Jeep Wranger Unlimited Sahara - 62k
2003 Gray Mercedes ML350 - 122k

Used to do long downhill runs in my old Triumph in neutral (Angel Gear) but that was a manual transmission...

Not thinking it is very good for automatics... Besides being illegal in most states...