Yes, the speed of a payout does depend on your selected cryptocurrency. Cryptocurrencies have different processing mechanisms, each featuring their transaction per second speeds
For example, BTC has an average of 7 TPS (transactions per second), whereas LTC has an average of 54 TPS. The more TPS a blockchain can handle, the faster your transaction will be processed.
Blockchains like Solana can handle 4,000 TPS, meaning that if 7,000 transactions are requested, they could all be processed within 2 seconds.
The speed of your payout depends not only on the cryptocurrency and blockchain you are using but also on how busy the network is at the time of your request.