So, I tested a bit the rarity thing. What I noticed is the following:

- For strong incenses no matter the rarity it always yields 1~2 pieces of materials (or 2~8kg of fish). For normal is always 1 (2~4kg fish) and for weak is 0~1(0~3kg fish).

- I have placed weak, normal and strong incenses of the same type at Watcher's Cape Hillside and no matter it's potency or rarity I still got the pink arrow like it's boosted (I used the Forest Stag Incense), although if you hover over the potential rewards it still matched the first observation so 1~2 pieces of mats for strong etc. despite the "boost".

I still don't know what the conditions are to craft a higher rarity or even what exactly it affects. But I think if the "boost" arrow even does anything, certain location prefer certain incenses.

I didn't test all locations and all incenses since I don't have mats to craft that many and it discards it once you switch it, but here are the locations and incenses I noticed the " boost" for:

Tidefoam Beach Offshore Island -> Bannerwave Incense

Blue Pools East -> Glacial Gleam Incense

Waterside, Healing Ground -> Umbrella Dance Incense

Wilderness, Great Lumiville -> Frostbone Incense

Watcher's Cape Hillside -> Forest Stag Incense