Here's an old detailed thread with worker count mechanics: https://aurora2.pentarch.org/index.php?topic=12258.0
Since Io's colony cost is 6.2, you will need to either use terraforming to get your CC below 5 or deploy orbital habitats. This is because the proportion of your population working in the manufacturing/mining sector will over time drift towards (25-5*colonyCost)%. This means that it is possible to have your worker pool shrink over time even as your population increases.
- A 0 CC home world will eventually settle into 25% of its population as TN workers
- A 2 CC plant will have 15% as TN workers
- A 5 CC plant will have 0% as TN workers
A couple of implications which may be relevant for OP and others:
- With a small amount of calculus, you can find that the peak manufacturing population occurs for a (total) population in billions of P = (0.76 - 0.04*C)^4, where C is the colony cost. For an Io colony cost of 6.2, this means the maximum manufacturing population will occur for a total population of about 69 million (nice!).
- For a colony cost less than 5.0, once you reach a population of about 240 million the services sector hits a maximum of 70% and manufacturing population increases linearly with total population. This means that, in theory, growing a colony with C < 5.0 will eventually allow you to exceed the maximum manufacturing population from the previous point, although for higher colony costs this may not be economical and the "lower maximum" may be a more realistic target. I would say colony cost of 3.0 or 3.5 roughly marks this boundary, but it depends on how willing you are to invest in growing a population beyond 240 million.
- A colony with C > 5.0 has a hard maximum manufacturing population, and you should not grow it beyond this point. In practice, you probably want to be within a couple million population in either direction and draw off pops/infrastructure from normal growth every so often to maintain the level. This rule applies for Io!
- For a colony cost less than 1.5, manufacturing population will always increase with total population.
Since ark modules do not have any agricultural population, the rules work a little bit differently, but suffice to say since the colony cost factor disappears you will always gain manufacturing population when expanding an orbital (total) population. Since Ark Modules cost a bit more than 500 infrastructure per million population, this means that Ark Modules are probably the most cost-efficient way to support a population for a colony cost greater than 5.0; for lower colony costs it depends on the relative importance of the infrastructure costs vs improved population efficiency, but probably a colony cost of 4.0 is a good approximate break point as a rule of thumb.
I would therefore recommend using orbital populations to colonize Io if you have researched and built Ark Modules.