Here is my take:
1. Julia was in the right to not tattoo the canvas. He signed the dotted line to get a free tattoo. He is NOT a client. He is NOT a customer. It is wrong to call him as such because he is not paying a dime for that tattoo. He is a simply a CANVAS for the show. This show has been around for a few years. Those who watched the show know that there will be limitations to what you can get tattooed on your body. The biggest limitations are time constraints, subject matter, and the abilities of the artist. These are considerations Julia's CANVAS should have thought about before signing up for a FREE tattoo, a tattoo that you would normally pay $600+ for. If Julia's CANVAS wanted full control over his tattoo, he should have saved up hundreds of dollars and paid for it himself. But because he wanted to be a cheapskate, and then bully an artist into tattooing an idea that would put her livelihood in the competition at risk, he is A SELFISH, ENTITLED PRICK.
2. Julia was in the WRONG for telling him to fuck off. Yes, the canvas was being overbearing and rude and micromanaging. However, his poor attitude did not warrant a "fuck off". She's clearly immature and has growing up to do with how she emotionally handles her stress and frustrations. I will not take sides on whether she lied to judges or not because I have not seen all the footage. As for her throwing a pity party: common self-defense mechanism for someone who needs some growing up.
Overall: Julia emotionally did not handle the situation well, but she was in the right to tell him to leave. I still think she is a much better artist than the other contestants give her credit for.
Unrelated: Emily needs to go back to whichever layer of hell she came from. Cleen Rock One needs to shut the fuck up. He is only at the top because the most of the other artists plain suck. If he was in the 2nd or 3rd season, he absolutely would not stack up as well against the contestants that season. I also hate his fucking teeth. Eric needs to stop being smug. He won 1 fucking flash challenge. That's it. He couldn't even win the ellimination round he handed out skulls fpr even though it was his speciality (Japanese).