Why does my solder not stick to the pads no matter how hot I set the iron?

Your temp is fine. 360 is a perfectly normal setting for leaded or lead-free solder on a kit like that. The beading and dull joints almost always come down to the tip, not the dial. A cheap digital station usually ships with a tip that's either not properly tinned or has burnt flux baked onto it, and a dirty tip transfers heat terribly no matter what the display says. The solder balls up on the tip because it's got nothing clean to cling to, and the joint stays cold, which is exactly why it looks lumpy instead of shiny.

So here's what worked for me when I started out. Get the tip hot, wipe it on the cleaner, then immediately feed a little fresh solder onto it so it's got a bright shiny coating. That's tinning the tip, and it's not optional with these stations. You should be redoing that wipe-and-tin basically every couple of joints. If the solder still refuses to spread after that, the tip itself might be oxidized underneath, and you can try a tip tinner paste to revive it. Beyond that, a fresh tip is a few dollars and fixes it permanently.

The other big one: put the solder on the joint, not on the iron. Touch the tip to the pad and the component leg together, hold it there a second so both parts warm up, then feed the solder in where they meet. If you melt a blob on the tip and try to smear it over, you get exactly the beads you're describing. The joint should pull the solder in like a sponge when the temp is right.

Dull and lumpy can also mean the part moved while it cooled, so hold still for a couple of seconds after you pull the iron away.

And no, don't bother tinning the pads first on through-hole work. Clean joint contact does the job. If a pad fights you, a touch of flux is what sorts it out, and a flux pen is cheap.

Funny, I ran into almost the same thing but with a battery powered iron doing little audio mods, no temprature dial at all. Turned out half my problem was just rushing. Once I actually held the iron on the pad and leg for a couple seconds before feeding wire in, everthing changed. Also the solder wire itself matters more than I expected, my first roll was some ancient spool from a garage sale and it behaved horribly. Got a fresh one and it flowed way better. No idea if age really does that or if it was something else, but worth checking what you're feeding in.

One thing I'd add is check what solder you've actually got. Leaded vs lead-free changes the whole feel of a joint, and lead-free is what looks grey and rough even when it's done right. I solder harnesses at work all day and we run lead-free exclusively, and new folks always think thier joints are bad because they've seen leaded joints online. If your spool doesn't say, assume lead-free and stop chasing that mirror shine. Also give the board a wipe with isopropyl first, finger grease on pads causes beading more than people think.

This whole thread is making me feel better about my own disaster board. I did the same thing with feeding the solder to the iron first, basicly glued my thumb to the blob trying to push it around. What fixed mine was way less pressure on the pads, I was mashing the iron down like it was a screwdriver. Light touch, wait a beat, done. Question though, how long is too long to hold the iron on a joint before the board itself gets mad at me?