No, this is completely wrong, and it's different from what you did, isn't it?
Please watch the first video that I posted a link to - Margaret gives a really good explanation of the Serpentine belt path as well as a video demo of what to do and what not to do and why. I know the seats in her video aren't the exact one that you have, but almost all the seats on the market with the two holes in the back like yours has fits this way, and none of them fit in the way that the Halford's employee has done it, and I can explain why. I'll do a bit of a diagram, hang on.
I've uploaded a picture of a seat of a similar type to yours - underneath the padding, if you take the covers off you can see there are two holes in the shell. This isn't necessary to fit the seat, it's just so you can see why I've drawn two black ovals on the diagram.
The second picture is my hastily drawn Paint diagram. You can see the line drawing of a similar car seat taken from a manual, with the holes drawn in.
The green is what you've done in your original picture from this morning. This is the CORRECT belt path. It's over the front of the seat at the two sides, then under and through the back for the middle section. Underneath this is a top-down view. I've made it very loose and wiggly in my picture so you can see where it's supposed to go, obviously IRL you would tighten it a lot more. You can see here that the bottom of the seat is secured because the lap belt is going through the "arm rests" of the booster part, the top of the seat is secured because the diagonal belt is going through the shoulder guide and the red clip on the left side, and the overall installation has tension because it's gone through and around the seat turning six times which allows the belt to hold with friction. If this fitting is loose in your car it might be because of the position of your seatbelt buckles.
The blue one on the right (and red underneath) is what the Halford's employee has done and this is a very common error but it is totally incorrect and isn't securing the seat at all. In fact, because the backrest and the booster seat part aren't actually firmly connected what they have done is simply connect the back but they haven't secured the base of the seat at all. It's also totally loose with nothing to connect and no tension because you haven't made any turns around the seat. It's very dangerous, definitely do not use the seat like this.
The manuals on these generic models are frequently confusing and it's difficult to see which part of the belt is supposed to be going over and which under, which is one of the big problems with them. I also can't find the right manual online and the fitting video on the Halfords website is of a totally different model of seat so it is no use.
I know I'm just a random person on a website, so I would recommend you don't take my word for it but contact one of the safety organisations such as Good Egg Safety or Child Seat Safety Limited.
https://www.goodeggcarsafety.com/
https://childseatsafety.co.uk/