Do they balance the wheel or the tire?

I had a new tire recently balanced.
Then it popped a few days later, so I get a used one.
They forgot to balance that 2nd tire.
But, I get no wobble, so I assume the 2nd tire is balanced.

Did the first balance address the rim itself or the rubber tire?
Does changing a tire immediately after a balance require a new balance?

Both. Supposedly the weights on the rim balance imperfections in both the rim and the tire. The weights are removed from the rim with the tire. All competent mechanics will rebalance. Perhaps the weights were such that you did not see them and maybe on the inside.

You can be lucky occasionally to find a tire that needs no balance weight. Consider too that a wheel alone could be imbalanced and with some luck an imbalanced tire could correct it.

Usually the wheel would be rebalanced when the tire is changed. But if you got no problem, don’t worry, be happy.

The tire popped? I’d like to hear that story.

Get the replacement balanced, you may or may not feel a wobble, but for a few dollars I’d want it balanced.

I’m with Texases on this one. If it begins to develop an erratic wear pattern it’ll be too late to correct it.

Sometimes you get lucky

http://www.bridgestonetrucktires.com/us_eng/real/magazines/ra_v13_i1/PDF/ra_v13i1%20ask%20doc.pdf

But the tire companies help you all that they can.

Just an FYI:

The Bridgestone article is about truck tires - 18 wheeler variety. What they say there is true for THEM! But is not necessarily true for other tire manufacturers.

This is particularly true in passenger car tires - where the markings are far less standardized (more manufacturers of tires and wheels, so more variations).

So do not expect your tires to have marks on them, but if they do, matching up the dots may be helpful.