It is an art for sure. Some of the biggest mistakes newbies make is.....they don't take the tourniquet off after the vein is punctured. If the veins are fragile, that back pressure is enough to blow the veins. In fact, with some patients, it's best to poke without the tourniquet at all, so-as not to blow the veins. It takes practice and knowing the patient to determine if that's the case, which is more difficult to do these days since most caregivers no longer have a relationship with their patients.
Also, when the draw is complete, it's important to apply good pressure to the insertion site after removing the needle AND lift the arm up to stop the bleeding, especially if patients are on blood thinners. I used to have the patients keep pressure on with the gauze and elevate, while I was preparing their specimens to go to the lab. Those couple of minutes can make the difference between having a goose egg vs. just having a small puncture spot. It's pure laziness not to do that.
There are some patients who are just gonna bleed or get welts. Sometimes the vein is torn and there's not a lot you can do about that. Typically it's patients who get poked a lot or have fragile veins. But, those seasoned nurses/lab techs know to make a swift insert and not root around for the vein.....get in, get the flash, take off the tourniquet, get your vile, and get out! Make it quick and make it smooth. Then....pressure and elevation! Even if your nurse/phlebotomist doesn't apply pressure and suggest elevation, I suggest you take the lead and do it yourself. Sadly, that's kinda like what healthcare has come to today.......kinda like the self checkouts.