You wouldn't normally say either of the phrases. If you wanted to tip someone with cash, you would likely pay an additional amount to the fee due and say something like, "thanks for the service", or "this is for you", or "keep the change". Likewise, if you were paying by card, you would likely say something to the effect of "round it up to X", "let's call it X".

As others have mentioned, anything and everything don't make sense in a tipping situation. If you're paying something by bank transfer, 'tip' probably isn't the correct word. I sent payment for your invoice and a (little extra)/bonus to show my appreciation for your efforts. In general, you would usually say 'anything extra' and not 'everything extra'. That's because it's smaller than the whole, and also might suggest that the extra could be small or zero. I contributed 2 cases of tomato sauce to the alumni banquet and told them to donate anything left over to the food bank. (something between 0 and 2 cases) We've covered our expenses. Everything we get from now on is profit. (Not different in meaning, but more optimistic than 'anything')