Notes
sRGB or CMYK: which one print-on-demand actually wants
It is a reasonable assumption that print work should be CMYK. For print-on-demand it is the wrong one, and the reasoning is worth understanding rather than memorising.
Conversion has to happen somewhere
Presses lay down cyan, magenta, yellow and black ink, so an RGB file has to become CMYK before anything is printed. The question is not whether that conversion happens but who performs it — and the answer determines how good the result looks.
The platform knows things you do not
A conversion is only as good as the profile it uses, and the right profile depends on the press, the ink and the substrate. A design printed on a cotton tee, a poly blend and a paper poster wants three different conversions. The platform knows which press and which material the order is going to. You do not, at the moment you export.
What to actually do
Set your export preset to sRGB once and leave it. On Merch by Amazon this is explicit — artwork is expected as sRGB. Elsewhere it is the safe default for the same reason. If your design tool is working in a wider space such as Display P3 or Adobe RGB, the important step is converting on export rather than just tagging the file, because a mismatched tag produces colours that look correct on your monitor and shift in print.
Frequently asked questions
Will my colours be less vivid because of this?
The opposite. Supplying sRGB keeps more colour information available to the conversion the platform performs with the correct profile. Converting early is what costs you vividness, and it costs it permanently.
What if my artwork is already CMYK?
Convert it to sRGB before exporting. Some of the original range is already gone and cannot be recovered, but you at least avoid a second mismatched conversion on top of the first.