re: "My first client hasn't paid me yet for last week work. Should I follow up him to pay?"
re: "Or would Upwork automatically send invoice to the client?"
If this was an hourly contract that you logged time for, you don't need to do anything.
Don't follow up.
And technically, Upwork doesn't send him an "invoice."
Traditionally speaking, an invoice is a bill and a request that the client pay a stated amount. Upwork doesn't really "ask".
Upwork just bills the client automatically. Upwork already has his credit card number. That's cool, because you get paid automatically.
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