WHat I do wonder is when I make a game wiht a non-expansionist civ, I usually make 2 Warriors and my gpt increase by +1gpt.
Presumably this is when you are initially building units @ 2 sheilds/turn (eg working a bonus grass) and in a city with no food bonus (ie food growth also @ 2/turn). This means that your second warrior coincides with your population growth so that now you have two citizens working tiles. I doubt whether you wil have roaded both tiles that your citizens are working but if they are commerce tiles with a base value above 0 (eg river tiles, lake tiles, tiles with certain luxes), which is not that unlikely, then that extra citizen will mean extra income. The fact that this coincides with a warrior build is just coincidence due to the rate of food collection and shield production! If you tried the same situation with a grass cow on your 8 tile initial city area, you would find that your income increased earlier-after 7 turns or earlier if you also irrigated the cow as your first worker action.
If this does not work for expansionist civs, it will be because you had popped some huts by then and had got extra settlers and/or warriors in play (or if none of your expansioist starts are by rivers). If you had extra units in play from a goody hut, then you could be exceeding your unit support, which is four units per settlement in despotism. For example if your scout had popped a warrior from a GH, the second warrior build would be creating a fifth unit (3 warriors, 1 scout, 1 worker). This fifth unit must be paid for but your income remains the same as before as its build (-1gpt) coincides with an increase in income due to population growth (+1gpt).
As you can see this is just me guessing as to what is happening but what I can assure you is that the reasons behind your observations are based upon other factors. You certainly do not earn cash for building warriors, not that this is what you were suggesting of course.
You can find out about your cash flow by using F1. It shows your total income and expenditure due to things such as taxes, unit support, deals with other civs, corruption, etc. The information below the top strip details what is happening at an individual city level. F3 shows your military and includes how many units you have, how many you are allowed and the resultant unit cost. Zooming in on individual towns shows you what each citizen is doing to contribute to your towns production in terms of food, shields and commerce. The latter is often overlooked by many players who then wonder why they are falling behind in tech!
Sorry for the boring response. I could carry on for ages about this but I can see your eyelids drooping so I'll stop now. I suggest you look out for the changes in F1 details when your first city grows in pop from 1 to 2. The answers will be in there somewhere!
