Voltage increase on regulator load
Probably you don't have a large enough capacitor on the output of your regulator to keep the voltage relatively steady. Try something like 1000uF. The capacitor gives the relatively sluggish regulator time to catch up. 

Your peak current could be relatively large- 8.4V/4 ohms is over 2A so the transistor will be limiting. 

Note also that the regulator cannot sink current- it can only source it- so without some kind of passive load (called preload in the regulator datasheet) the regulator will tend to err on the high side. A capacitor will smooth it out so that's less of an issue.