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This will depend entirely on the conditions of your insurance policy. Settlements can be handled both ways.
Most travel health insurances sold in Germany for use abroad do not pay directly to a foreign health care provider, but require the insurance holder to settle the payment on site and get a bill for the services, which will be reimbursed later. This can of course be quite inconvenient, as such bills can easily get much higher than what many tourists are able to pay unexpectedly.
Only some health insurances allow a direct settlement between the health care provider and the insurance, their foreign office or local representatives.
The same will be the case for travel health care insurances sold to foreigners for use in Germany.