If you just downloaded Pirate101 onto your computer, then it has to load and render multiple files and such. I'm not a computer expert, but my best guess is that when you did the tutorial, it was still loading many parts of the game, slowing down your gameplay. After everything has been loaded, performance should improve. Of course, it could be something completely different, in which case you might want to contact support.
It took me one hour to complete the tutorial + get the ship because it's incredibly laggy!
I don't have a slow computer, wizard101 strolls excelently so I have no idea. Does this always happen when it's your first time playing?
It could be that you are on a full server, it wasn't too laggy on my first time on the game, but that's because I started the game as soon as it came out. If it's your first time playing it could be that your computer is still loading up some things in the background like maybe then new update patches, it might be that your computer is loading many things at once. Have you got any other application software open? It could be that your computer is slow due to multiple applications being used. When I log onto the game it's a bit laggy for a few seconds but then it's completely fine.
For me, the tutorial wasn't laggy but when I first joined everyone else in the real game then it became pretty laggy at first. It still is laggy for me some times. I'd say about 9.7345% of the time the game is laggy for me.