Does an equal-time rotation make me resident in the host country?
It can, and that is the whole difficulty with rotational work. An equal-time rotation puts you in the host country for roughly half the year, which is precisely where residency tests and treaty employment articles turn. A handful of days either side of the line can change the answer, so the position has to be built from a day record rather than from an impression of the pattern. Count arrivals and departures, decide how part-days are treated under each country's rules, and keep the rosters and boarding passes that support the count. Near the line, expect to have to prove it.
Do my travel days count towards the host country's residency test?
Each country answers that for itself, which is why the same rotation can be counted two different ways. Some rules count any day of presence, including a partial day of arrival or departure; others exclude pure transit. The problem is not that either rule is wrong, but that a worker using one count for both returns ends up with an inconsistency neither authority accepts. The practical method is to record the movement once, apply each country's counting rule to that same record, and keep both tallies on file. The underlying record is the thing that has to be reliable.
My employer withholds abroad and my home country gives no credit, why?
Usually because the claim is not yet supportable, rather than because the credit is unavailable. A credit generally needs the foreign charge to be a tax on income, borne by you, and final. A deduction on a host payslip with no assessment behind it fails the last part, and over-withholding you could have reclaimed abroad tends to be refused at home. The route is to settle the host position first, obtain the assessment, and claim the credit for the tax actually due there. Where the host state should not have taxed the income at all, the claim belongs there, not at home.
Which country taxes my pay while I am working offshore?
It depends on where the work is done and on which article of the treaty covers the installation you are on. Offshore and resource activity is not always dealt with by the ordinary employment article, so an assumption carried over from onshore work can be wrong in either direction. Sourcing the pay by worksite, rather than by who runs the payroll, is the starting point. Then check whether a special provision applies to the waters you were in. Your employer's withholding choice is evidence of what it concluded, not a determination of the question.
Do days off spent in the host country count against me?
Generally yes, for presence tests. Those tests ask where you physically were, not whether you were working, so a break spent resting at the host base counts much the same as a hitch spent on the installation. It matters, because staying in country between hitches is often the difference between sitting comfortably below a threshold and going over it. Sourcing of the income is a separate question and follows workdays. Keeping the two counts apart, days present and days worked, is what stops one of them being used to answer the other.
What records do I need to prove where I worked each hitch?
Rosters, crew change records, flight itineraries and boarding passes, and the employer's own record of which installation you were assigned to. Build the year as a continuous day-by-day record while it is still recoverable, because reconstructing a rotation from memory long afterwards is the point at which most positions fail. The same record answers residency counting and income sourcing, so it is worth keeping once and keeping properly. Where a hitch was extended or a crew change delayed, note why: unexplained gaps in a day record attract more attention than the days themselves.
Is double taxation legal?
Yes. Nothing prevents two countries from taxing the same income under their own domestic law — each is exercising its own jurisdiction. What treaties and credit systems do is relieve the outcome rather than prohibit the charge, and relief is generally something you must claim on a return or a form, not something applied automatically. Miss the claim and the double charge stands. Double taxation explains the mechanism.
How would a foreign tax authority know I am resident there?
Mostly from information you or your bank already provided. Account-opening forms ask you to self-certify tax residence, and that certification is reported between authorities under the Common Reporting Standard or, for US accounts, under the FATCA framework. Beyond that: employer and payroll filings, property registries, immigration records and the tax filings of anyone who paid you. The realistic planning assumption is that the data arrives. See FATCA and information reporting.