A magic item supplies its own magic
Most magic items don't interact directly with any magic or supernatural abilities a creature has on their own (though there are exceptions such as class-specific items like a Rod of the Pact Keeper). Rather, the item has its own magic "built in", such that it can be used by any creature, even those with no magic of their own. The DMG doesn't have much to say about this in general, but it is specifically confirmed for certain classes of items, such as (all emphases added) potions:
Different kinds of magical liquids are grouped in the category of potions: brews made from enchanted herbs, water from magical fountains or sacred springs, and oils that are applied to a creature or object.
Most scrolls are spells stored in written form [...]
A scroll is a consumable magic item. Whatever the nature of the magic contained in a scroll, unleashing that magic requires the user to read the scroll.
Regardless of explicit confirmation like this, all magic items, unless otherwise noted, work regardless of any magic the user may or may not have. So, a magic bean planted by a divine avatar should have the same effect as a magic bean planted by anyone else. It shouldn't matter who planted it.
Gods don't have to follow the rules
What might matter, though, is what the nearby avatar of the harvest god is thinking about while the seed is planted, regardless of who's doing the planting. If the avatar's thoughts and feelings have the power to shape the world like a god, then their will could influence the bean in some way, since it falls within the harvest god's domain. (And of course, the avatar might have stronger feelings about it if they are the one doing the planting.) The specific effect of that influence is entirely up to you, the DM. You could roll for the effect normally and then amplify the effect, or keep re-rolling until you get a result that the avatar would find favorable, or cause an effect that is not on the list entirely.
If your goal is to use this event to hint at the nascent divinity of the avatar, then regardless of what happens, you can narrate the effect in a way that makes it clear that some external force is influencing or enhancing the effect of the bean. For example, if the chosen effect is that a single tree grows, you might narrate the single tree growing, then pause just long enough that the players think the effect is done. And then suddenly the tree's roots grow out to the sides and sprout three more trees.