Well yeah, when you applied they did an inquiry. Then they approved you instantly based on what the inquiry showed them.
Yes this is the normal process of applying for credit. All my applications has resulted in HP, either the same day or the next. When one apply for credit he/she should automatically expect it to be a HP. However, there is one exception the SCT, with Comenity.
Their computer checked your credit. That's how it decided on whether to approve you or not and what your terms would be.
New inquiry is possible even when a card was instantly approved ?
An instant approval doesn't mean that your credit was not pulled. You should expect inquiries when applying for new credit.