Yes, stop but also understand
I will give an example. Many years ago I worked for a company. My "On paper" hours were 9am to 5pm. However I had a responsibility for a task that needed to be completed at 7am. So I worked with my manager to adjust my hours to 6:30am to 4pm, and "always" get overtime.
Several months into the arrangement I had replaced the task that needed to be done at 7am with a computer program and VPN access to monitor that program. I adjusted my hours (with the manager again) to 11am to 7pm. This allowed me to work more efficiently, as I missed all the "arriving times" of everyone that would "hey could you do this for me real quick" allowing both of us to sidestep an issue (that people would actually do that).
Several months later, we adjusted this again to 1pm to 9pm because I like working later, and we had a client in a different time zone that needed the support during that time.
A couple months later, we adjusted back to 11am to 10pm with no Fridays. The client support was no longer needed but we discovered that having someone around latter was often beneficial.
The entire time, my stated, on paper hours were 9am to 5pm Monday - Friday. My manager caught some flack over this and had to do manager things, (including pointing out to other equal managers that having me there at night was a benefit to them too).
When I was promoted to manager of that department, I made the same arrangement with team members. Everyone worked different hours even though officially, the paper work said 9am to 5pm.
The point is this. You don't know what is going on. There could be similar arrangements, different needs, or odd requirements. Until you can full understand what is happening with people coming in at different times, then you should be there at your allotted time, and leave at your allotted time. If you were to show up constantly late to an internship that I ran, I would let you finish the internship (cause I would want to maintain good relations with the school), but it would not turn into a job offer, and I would not be a reference you would want to use on an application.