I did some reflow soldering using "ZB" brand small reflow oven (probably around 100 times), heated plate and hot air. I think that OP different heating method hypothesis may be right. Unlike DIY reflow oven, semi-professional reflow oven doesn't have a glass door window for inspection, so there is no way to say what's going on there. My observations: a new "Mechanic" brand Pb-paste gives factory quality solder joints, with a very few solder bridges caused by my imperfect paste application. No easy way to see what's going on during melting process without opening the oven.
Heated plate allows visual inspection during heat-up. In this case paste melts badly and covers solder mask, adjacent pins melted paste overlaps, etc. Again, I don't know if this happens in my reflow oven and then somehow fixes itself. But for obvious reasons we can conclude that components and their pins temperature is lower than PCB surface temperature. And PCB surface temperature is lower than hot plate temperature. Obvious reasons are: imperfect contact between these three objects, and cooling of everything of top with surrounding room-temperature air. So my speculation would be that in infrared reflow we have opposite temperature distribution: chip surface and pins heat up faster than PCB surface, because components shield underneath board areas from infrared radiation (shadow from components). Sooner or later every will heat up to the same temperature, but there is still some time difference between what heats up first This may affect behavior of melted paste. In reflow oven (heating by IR element from above), paste melts and have opportunity to "climb" a little on the heated pins first, and only then soldering pads heated up, maybe with very small 0.5 second delay, but this delay may be enough for a totally different outcome. Imagine a water droplet on the window during the rain: if you "help" it with a toothpick to move in a certain direction downwards, e.g. lower-left, then it trajectory would be altered and there is no way for a droplet to "climb up" and go through unaltered trajectory. Or a small piece of ice on a frying pan with a screwdriver touching it from above. Outcome would be different for two cases: if you heat-up frying pan first, or heat-up screwdriver (e.g., with a lighter's flame). I am not sure if this logic may be applied to solder paste melting process, but thought this idea may be worth sharing.
Another observation, this ugly overlapped melting is not always caused by excess amounts of applied solder paste. In my case, I observe that solder joints of 0805 components are very small, and kind of solder-starved and asking for more solder. This makes me think that the second OP hypothesis about heating profile may be right. But I don't have explanation for this. I can't understand how this melted paste volume may be decreased with a preheating. Evaporation? Probably not.
It seems that professional factory reflow soldering process achieves good results thanks to hood preheating and rapid speed final heatup. First, solder pad and pins are heated to some temperature right below melting point, so everything is almost prepared to be wetted with solder. Then, everything is heated up rapidly above melting point, so pad and pin are heated up above melting point and wetted with solder simultaneously. Melted paste to goes in both directions, and there simply no more liquid state solder left to escape and cover solder mask area.
To sum up, it seems that we need to preheat everything right below melting point and keep paste in non-liqud state. We are doing it slow and wait until everything settles around some common temperature value. And only then, quickly ramp-up temperature. In some sense we are trying to make solder pad and component pin heat up similarly to soldering iron tip. If final heat-up is too slow, or something heated slower, there is a chance that liquid solder escape joint area. With a heated plate it is very difficult to ramp-up this temperature due to poor thermal contact: pin is thermally "isolated" from heat plate by PCB itself, and by thin layer of paste. Adding additional flux often improves DIY reflow, probably by reducing thermal resistance and improving wettability. With infrared reflow, we can illuminate pin and uncovered pad area much faster and almost simultaneously.
problem 1 to be solved:
if pin or pad temperature raise have significant time lag, then we have excess of liquid solder during this lag. E.g,. pad heated up properly, but pin is too cold. Liquid solder only bonded to pad, but not to pin, like component is not there. Moreover, "cold" pin prevents solder to form a half-sphere droplet, by tipping into middle with it's non-wettable surface
problem 2 to be solved:
final heat-up is too slow. If final temperature raise rate is slow, then paste goes to liquid state while pin and pad are not wettable. In some sense, during this period pad is not different from solder mask, because there is no bonding. If we cool down things at this stage, solder is easily peeled off from pad. Very similar to faulty solder joint made by poorly heated soldering iron tip.
In short, heat-up everything to below-meltimg point, then do some "shock" rapid heat-up to make pads and pins work as mini soldering iron tips, their surface must become wettable fast, preferably before paste melted.