My DS is exceptionally good at maths, and we are now Year 1 in a state school.
Now I've seen the shift to a Year 1 more formal classroom environment, it has really cemented to me how Reception is solely play based, exploratory learning and an introduction to school really. Settling socially and gaining independence (looking after all your things and being able to manage the school day) are as important as any learning.
We had such a conversation with the (excellent) reception teacher and she pushed him as much as boundaries allowed. He was calculating 2 digit sums while others were doing 1, he was given the Numicon teachers resource set to play with, as the standard set was too small for him. She encouraged me to buy that set and gave us some additional activities to do at home. She said the key at this stage was to full make sure he understood what the physical values actually were, as well as being able to do the sum. I must say, I don't think I needed to have had that conversation, as he would have been identified anyway, but that's not the case with every teacher/school.
To add to this, at home I've taught him the time, play extensively with money, bought time tables flash cards which he's pretty much learnt too. No pressure, just added these in as games for him to try. Also look up the app Scratch Jr, as I've started to teach him to 'code' his own animations. Another area to explore that's mathematically related.
In Year 1, he is much happier in the more formal room setting, and is being set maths worksheets offering different levels of difficulty. At this stage he's doing +1/-1 and I think counting in 2s/5s/10s will be coming soon. He can already do all of this, but I don't really see the massive need to be pushing him excessively ahead of others in the school environment.
I'll be talking to the new teacher at parents evening about this in a couple of weeks, but most likely expect to be doing additional maths work/games at home rather than expecting the school to bump him up a year or two.
In the meantime, I've bought a Letts 6-7 maths book to do with him at home. This is as much to practice his writing of numbers, as he can do the maths but is still struggling to write certain numbers the right way around (left handed issue!)
Personally, I think the suggestion of getting a tutor at this stage is completely unnecessary. Let him enjoy his introduction to the school environment, add some additional maths play at home and also consider focusing on other areas that he may not be as strong in (reading/handwriting were two for us).