I''m not sure what your referring too???? 4-5???? Are your talking about your reading in DKH or Meq/l???? It really makes a difference......You said your water in the DT tested between 8.2-8.4???? That to me is alot of gray area.....is there anyway you can narrow it down a bit more?? 8.2 IMO isn't a bad PH.....I think running at 8.4 is alittle high though.....I think the big thing is keeping it steady than rather shooting for that perfect 8.3.......
Honestly I don't believe rinsing your test tubes with tap water would make a whole lot of difference....I always rinse with tap water myself, but shake them a couple of times before adding my sample solutions though........
Alk can be adjusted several ways.....If I have on hand I use Kent SuperDKH buffer, and baking soda will work just as well.....Any chemical addition needs to be done slowly and monitored......At times it may take a full 24hrs to get an accurate reading on the adjustments you've made to the system......You also have to remember that if your PH is running at 8.4 like your tests might be indicating, by adjusting your Alk you could possibly raise the PH even more....I've done some playing with meters and by mixing buffer and adding to the system you can easily see on a meter how the PH jumps rather high, but you'll see it come back down.....I don't know with your situation with your PH on the high side by trying to raise the Alk if you'll drive the PH higher....
I would honestly try to get a specific PH figure, even if it means buying a new test kit, a PH monitor or having the LFS test it for you to give you a good base number to start with......All numbers should be looked at carefully before tinkering IMO.......Another good possible way to get things back in check safely would be to do a series of water changes......That way it could balance itself out naturally....