Just be honest with them
The easiest way for everything to go well is if you are honest with them and tell them well in advance what this first session will be like. My experience has been that players are much more receptive to "scripted" events if they know it's coming, especially if they know the world will open up a bit later.
This does not mean that you have to say what will happen, but that the first session is still preparing the scene. You can always surprise them without keeping them completely in the dark. Tell them well in advance that some events of the first session will happen, they can not change that, and that everything is to set up for the rest of the campaign.
Give them the freedom to follow their orders
Even if the characters receive orders that they are supposed to follow, that does not mean that there is a specific way to track them. By offering them different ways (or letting them cope) to carry out their tasks, you give them enough freedom so that they probably do not feel guided. If you manage to make their choices impact the events of subsequent sessions, your players will probably be very happy to have been able to shape the world during their first session (with script)!
I myself am a new DM and I only have a few sessions under my belt, but that is how I approached the match up to now. I discovered that my players were very forgiving when I'm honest and forthright with them, and they are much more likely to trust me when I obviously hide something from them. I can not guarantee that your players will act the same way, but I can say that it worked with my group.
To clarify to which question I answer:
Note that I answer the question in the description rather than the title. For what this relationship between gameplay and cut-scene should to be, I can not really tell you that. It really depends on what your players like and your style, although I personally prefer to avoid using as much cinematic equipment as possible.