My son does this with my husband. He's showing you he misses you, and is desperate for time with you, with your undivided attention.
In my house, when my hubby gets home from work, he changes clothes and then immediately has to give at least one hour of undivided attention with no distractions to our son. NOthing else is as important during that time so phones go off, because there is nothing that can't wait an hour. After that he can do as he pleases until bed time, because he's the only one my son wants at night.
This helps curb the "look at me" behavior so energetically displayed in 2yr olds. Some of it will not go away, but it can help to avoid the full melt downs.
Also, toddlers don't understand not to interrupt. You can tell them to hold on, but at this age they are VERY self absorbed, and ALL needs are immediate. This is normal. We try not to ignore our son if he asks us a question and trys to get our attention because doing so or making him wait more than 3 minutes for an action(more than 1.5 minutes for a response), can only aggrivate the situation. He cant help it, this is neurological. I'll usually tell whomever im talking with to hold on, answer the boy and then go back to what I was doing. It makes life a lot easier, as there's time later to explain not to interrupt or to explain and teach the difference between polite and rude, until perhaps they have the emotional/social maturity to understand the nuances. Right now, it's not in his vocabulary. Doing so now is only going to make having a conversation with another adult harder.
If he's really acting out, and going from 0-60 there's something up, and you should probably stop what you're doing and remember that nothing's more important than time with your son. You'll be glad that you spent the extra time focused on him rather than visiting later in life, because in a few years he's not going to be so interested in spending time with you.
If he continues the behavior after getting your attention, then you can discipline the tantrum. But if he's just letting you know he want's you than what's so wrong about giving in? What's more important?