When he finished his solo mission. Did he leave or did someone ask if they could play next? The way I'm reading it. Sounds like the former.
You said you got 3 dances in. I can only assume you played 1 credit switching between your friends. 1 credit giving you 3 songs or how ever they have it set at DnB for how many songs per credit. Normally the case is, 1 credit for 3 songs for one person. Let the next person play. This is probably why he came by and swiped his card in for a credit on the machine. He probably thought you guys were gonna be there for a good half hour or more playing because you kept on switching. And that explains why he did what he did.
Full mode? I can only assume you mean doubles. It's been a while since I've played ddr. But when you played doubles. You had to pay 2 credits to play this way. Now if he were to play singles and one of you jumped on the available dance pad to shadow. That is very disrespectful to the other player. DDR pro or not, without asking if it's alright with the person paying for their songs. Having someone shadow next to you and you have no idea who this person is. Is very distracting and rude. It's like stepping into someone's personal bubble.
To respond to what the other poster posted. The proper Arcade ettiqute to show that you're next in line to play the game is. You leave a marker on the machine indicating that you're next. When I was playing we use various cards. Nothing you would worry about losing. But enough to know it's yours. I've used business cards, reward cards, etc. Don't use, and it should be obvious. A debit/credit card, your driver's license, social security card etc. This is just so everyone has a clear understanding that there is an order to get on the machine. Once you get up to play your game. You move to your card to the back of the line. We usually go from left to right. I can only assume you have a DDR Ace machine. If so. Look at the image below.
Do you see where, I think the yellow towel is. That's where I would start this indicator that you're next.
If it's a classic ddr machine.
Where it says player 1/player 2. Right underneath there is a little lip that you could put your placement indicators on.
I hope this helps you out and you're able to make friends with this pro in the future.