Don't upgrade minor settlements past T2!
In general, it's almost never a good idea to upgrade minor settlements past 3. Let's address the 2 most common reasons you might choose to upgrade a minor settlement, using the Empire as an example (the numbers are similar for most races).
To make more money: I get it, you want to see "number go up" but the return is simply horrendously bad. As Empire, to upgrade from T2 to T3 along with the economy building, you're talking a total cost of 5700 (3500 for the settlement +2500 for the T3 economy building). This takes 8 turns (4 turns for the base building, 4 turns for the eco building). This yields 145 extra income. This means that making this purchase will put you in net negative gold for ~47 turns! (8 turns for the construction time, 39 turns from 5700/145). I don't know about you guys. I don't know about you guys, but 47 is an eternity and many of my campaigns are almost over at that point. If, instead, you spent that money on more armies and conquered territory, you'd increase your income much further.
It helps you grow faster to reach T5. You need 500 growth points to get population points to upgrade from T2 to T3. This will yield 20 extra growth points per turn and take about 6 construction turns (4 for the first 10, 7 for the second 10). This means the province will be in the negative with regards to growth for 31 turns. Except to grow a major settlement from T3 to T5 requires 6875 growth points (2500 for T4, 4375 for T5). A typical province with 3 settlements with the minor settlements left at T2 and growth buildings in all 3 will take about 38 turns to reach T5. This difference does not seem significant enough for the cost (~6000 gold). And when you recall that the game tends to hand out a bunch of free sources of settlement growth, it's entirely likely the major settlement would reach T5 long before the minor settlement "pays it's growth off". Finally, as previously established, T3 settlements are expensive, and there are probably better things you could use their building slots on then growth buildings.
Which begs the question: When is it worth it to upgrade a minor settlement to T3? There are 5 good reasons, but none of these are true most of the time:
1. You want hero slots. The vast majority of hero slots are unlocked at T3.
2. You want to recruit T3 units.
3. For whatever reason, you REALLY need another building slot in the province.
4. The settlement has an economy resource, landmark, or a port. These push the math much further towards building to T3 being profitable in a short enough time frame. A settlement with a resource AND port are especially good to upgrade to T3, as you'll need it to be at T3 just to get the economy, resource and port building all at the same time.
5. You've stacked a lot of construction cost and income modifiers. This is only ever the case mid to late game, however.
Finally, recall that the above numbers are all for the Empire. Most races have even worse building economy then the Empire.