My apologies if this has already been answered, I couldn't find it if it has.
Ability score improvements seem to be tied to specific class levels. For example Fighters get ability score bumps at different (or rather additional) levels than Rogues. But lots of other things are tied to your TOTAL level. So what about ability score improvements? Fighters get them at 4,6,8,12,14,16,19. Rogues get them at 4,8,12,16,19. WIzards the same, 4,8,12,16,19.
So if you multiclass which level do you use? Total level or class level? If it's total level, which class do you use? Your first class? Your class with most levels? And if it's class level then under certain circumstances, you might go a long time with no ability score improvement. For example, a Rogue 3/Fighter 3/Wizard 3 would not get ANY ability score bumps. Is that correct?
Also, I have no dog in this fight. I don't mind either way. I'm just curious if this is a known answer yet. Thanks!
My guess is that it's tied to class level. That way, the Fighter 3/thief 3/Magic User 3 class sacrifices stat increases for flexibility. Probably a balancing factor.
When you reach a level in a respective class, you get whatever benefits it gives be it feat or features, unless noted otherwise in the multiclass rules. (ex. Extra Attack)
Here is my best guess. Total level will refer to your profiency bonus. Each ability score improvement is obtained just like class features. For example, if you are 8th level character that is a 4th level fighter/4th level rogue than you get two ability score bumps. Also, I am guessing the total character level remains at maximum of 20.
Yes, I believe your example is correct. A rogue 3/fighter 3/wizard 3 would not get any ability score bumps. I guess that is the trade-off.
Thanks for the answers and insight. I really appreciate it. Seems like everyone agrees. Wish they were all this easy. 
If I were making it, I'd have the seemingly standard ability score advancements (4, 8, 12, 16, 20 ... I mean 19) be tied to character level, and the ones that stand out otherwise be tied to class level. 6 and 14 are bonus ability score bumps for being a fighter, for example. But unless the multiclassing rules say that, that's just my desire.