that is my personal preference, but I hesitate to say it is by far the only way to do it because as soon as I do, 10 people will jump on with alternatives and reasons to do so... but you got to decide to do something.
My suggestion is to experiment liberally as you are doing this thing and take good notes of what works and what doesnt. Your grow space and your way of doing things is different than anyone elses, so you need to figure out what works for you.
You can really put them under the hps anytime after the young things can stand the light, and even then you can put the light way up high so as not to burn them. HPS is fine for now... and if you talk to them in Europe a lot of people use HPS all the way through and claim it to be superior.
I hear a lot of rumors that begin with "I was told..." There is not a race to up pot. To decide when to up pot you have to ask yourself, why did we down pot? Why do we start in a smaller container and move up... why not start out in a 10 gallon? Well you know by now the reason is that we are working on building up the roots. So that smaller container is a restriction of a kind, so as to build up the best roots that there ever were, right in that tiny space. It is well controlled by your proper watering, and there is no advantage to moving out of there until something tells you that is finally causing a problem to be in that tiny space that you are filling up with roots.
Think of your soil as a buffer that allows you to suspend water and nutrients in, for the plants. At first that buffer gives you 3-5 days where the container does what we put plants in a container for, it automates this process for you for 3-5 days. But soon that root ball becomes able to suck up that water faster and faster, diminishing your buffer time between needed interactions with the container. The reason... and the rule as to when to up pot, is when your buffer goes to 24 hours. When the plant can finally use up all the water you can put in that container, in 24 hours, it is time to up pot. It is just coincidental that in some plants and sometimes and in some containers, the diameter of the leaves extending over the cup edge happens at just about this same time. One method of understanding why we do this is a guess... the other is a valid scientific reason.
Now having said that... early in my learning curve... I too spoke about the circumference of the leaves in regards to up potting... we all have to begin somewhere.