Hoping for a refund

I was tired of my university free student tutoring was wanted to try a professional tutor instead. I was setting up a plan with the phone operator and she asked for my debit card credentials to make a 8 hour plan for over 600 dollars. When she made the payment I was unsure that I wanted to spend that much. Originally she transferred me to customer support and while being transferred they hung up or lost connection. I was worried that they scammed me so I called back and everything seems to fine while getting the refund in order, but I have to wait around 5 business days.

They recently called and to make sure that if I changed my mind if I wanted to go forward with the tutoring today but I said no. I’m just worried if I’m being scammed out because everything seemed to be very fast with the payment. Or is this something that’s normal for them and legitimate?