Hi L2pull, and welcome to CoffeeSnobs,
Your on the right track, 10 seconds is too fast.
Firstly the filter basket that you describe is commonly fitted to the cheaper machines, and does not normally require as fine a grind as some other baskets.
Secondly, which basket are you using, the single or the double?
Singles can be quite hard to get a decent pour from,
usually better to use the double, even if only making one drink, especially with some of the smaller double baskets typically used on those type of machines.
Thirdly, was the puck wet and sloppy or relatively firm and dry after pouring?
If the puck was wet and sloppy, then you need to dose more into the basket.
Generally try to fit as much in as you can and still get the portafilter onto the machine, this will help in extending the pour time....suggest try filling basket, tap portafilter on the bench once to settle the grinds in the basket and put a bit more in, then level off with finger or kitchen knife, then tamp
How much are you tamping, the common 30lb/15kg is a bit much for the type of basket you have, but harder tamp can help extend pour time.
If all this doesnt make much difference, then yes you will need a finer grind, assuming you buy same beans/roast type again.
Final suggestion is to plan to get yourself a grinder, surprising how well you can make coffee on the cheaper machines if you have your own grinder to freshly grind the beans just before you brew.