I gave up my CPA, but in general (as many have said), your home/resident state (if it has an income tax) taxes all income earned. The nonresident states where you earn money only tax for the portion of income you earn in those states (based on an apportionment formula of % earned in that state/total earned). There are a few methodologies for apportionment (e.g. duty day method- days worked in state x / total days worked)
To alleviate double taxation, on your resident return, you get a credit for taxes paid to other states (though there are some nuances like the credit calculation is based on if the income was earned as a resident so you wouldn't get the full credit if your resident state was a low income state and you earned income in a high income state).
There are also some nuances. I don't know about the jock tax specifically, but many states has reciprocity agreements. For example, MD, DC, VA and PA have reciprocity so if you were a MD resident working in Virginia, as long as your only income was wages, they would be treated as MD income and you wouldn't have to file in VA.
So if you live in MD and work for the Flyers, theoretically, you would still just pay MD income tax for what is earned in PA (though Philly has its own taxes)?
There are so many state/locality specific rules.
Signing bonuses are complex, but you should google "signing bonus planning for Canadian and US professional athletes" for an RBC article that explains things pretty well. The US-Canada treaty comes into play.
International tax is generally similar to resident state taxation. I think both the US and Canada have a "worldwide income" approach where residents are taxed on your worldwide income and then get relief from double taxation via tax treaties/credits for taxes paid to other countries.
This is just some general information. Individual scenarios are specific (obviously).
Tax day is only 37 days away thankfully.