Visitors First Action Time (no replies)

I'm wonder what happens in the following scenario. Let's say a visitor visits our site on Monday and just browses around and then returns on Thursday to make a purchase. We are seeing the "visit_first_action_time" being shown as the first visit on the second day and not the overall initial visit. Is this the designed behavior and if so is there any work around or suggestions to get that initial visit time?

Thank you!
Marcel