EX, EQ and TU do not decide how to designate an inquiry. The creditor designates the type of inquiry at the time it is made.

Many lenders will pull account review inquiries immediately after an account is opened, or a week afterward, or two weeks, or all of the above. Amex, especially, is known for a large number of soft pulls.

However, I stand by my statement that in the majority of cases, there is one hard pull - on one of the three bureaus - per new application. Sometimes two. (AFAIK, Capital One is notorious for pulling all three, but virtually no other banks will.) However, it's also known to happen that some banks don't pull again if they already have a recent report on file, according to their own criteria.

However, to state that lenders other than MBNA simply do not pull hard inquiries is misleading advice, and will not be true for the vast majority of people.

Usually inquiries shown to credit monitoring services are hard inquiries, so the EQ inquiries you're seeing may well be hard. (It depends on the specific service you're using, though.)