Hi A., I am a specialty painter by trade. Any time 'jewel tones' are the paints of choice, you definitely should prime your walls. And, yes, tint the primer to work with your base and finish coat colors. Primers only can take so much colorant, so you get pink (for the wine red room) or grey-ish blue (for the dark blue room) in your case. Your paint store rep will help/advise you on this. Be aware that jewel tone paints require 2-3 coats, depending on the manufacturer. The base for these paints is usually a 'clear base' (almost transparent). Some of these type bases are 'dark bases' for darker blues. Thus the need for more than one coat to achieve the desired look. Most of the other paint tones start out with a white base (non-clear), prior to the tints being added. These usually cover with 1-2 coats depending, because the base starts with pigmentation. Jewel tone colors will intensify their depth and beauty with two-three coats. (Note: I would allow a 24 hour drying period between each coat.) If these rooms are painted with the proper steps and care, they should be fantastic. Off set these deep, intense colors with contrasting colors, furniture in your rooms. I hope this is helpful for your project. Have fun with this, take a deep breath, and...Happy painting! ~T.