Is using RAM from two different manufacturers likely to cause
No, it won't.
Just make sure that both pairs are installed in the correct slots to enable dual-channel memory to work correctly. The two remaining slots will almost certainly be the ones to use for the new pair. In addition, motherboard RAM slots are nearly always colour coded so each pair is installed in slots of the same colour.
There is an argument that you plug the larger value RAM sticks into the primary slots to get a marginal speed gain.
I think that the likelihood of a human being able to notice the difference is rare.
You should note that if the two sets of RAM are of different speeds, the whole will run at the speed of the slowest. Again, I'm not sure that the average human would be able to tell the difference and you are more like to get an added advantage from the Gigabytes than you lose from the reduced speed.