Thanks to The Mystical One for posting this on the forums.

This 100% came from yab on the GameFAQ's forum:

I came across this information and I remember in the last thread people were interested in it.
As most of you know, the fountain opens up after fully upgrading your inn (30 guests) and there are four spots where you can get items.
For every 100 tags you get, you'll get an additional item up to 14 spots at 1000 tags.

The items you get are either from the common items, or from one of the special item groups.
The special group you are in is fixed per game.
You may be able to get different items temporarily if you join another world, the host goes to their fountain, then you leave and go back to your fountain.
You may also find items from other groups after tagging others.

Common items:
Medicinal herb, Holy water, Angel bell, Emerald moss
Narspicious*, Resurrock*, Astral plume*, Mini medal*

Special items:
Grass group: Flurry feather, Ice crystal, Softwort, Superior medicine, Thinkincense*, Yggdrasil leaf*
Stone group: Flurry feather, Ice crystal, Rockbomb shard, Corundrum, Flintstone*, Mirrorstone*
Sea group: Lava lump, Evencloth, Seashell, Crimson coral, Panacea*, Mystifying mixture*
Ore group: Lava lump, Evencloth, Iron nails, Iron ore, Platinum ore*, Mythril ore*
Sand group: Brighten rock, Royal soil, Glass frit, Kitty litter, Saint's ashes*, Malicite*
Flower group: Brighten rock, Royal soil, Sleeping hibiscus, Nectar, Lunaria*, Enchanted stone*
Water group: Thunderball, Fresh water, Wakerobin, Nectar, Magic water*, Sage's elixir*
Mushroom group: Thunderball, Fresh water, Fisticup, Belle cap, Aggressence*, Finessence*
* - post-game only

The group you're in also affects how many shining spots you will get at field spawn points, so even if you don't have a fountain, you can find out by checking these locations.
But this list assumes all points have spawned, so you might see less than these amounts unless you've left your game on for a while:

Fisticup (SE of Stornway)
8: Sea
6: Flower
5: Water
4: Stone
3: Sand, Mushroom, Grass, Ore

Lava lump (NW of Alltrades Abbey)
8: Sand
6: Mushroom
5: Grass
4: Sea
3: Flower, Water, Stone, Ore

Royal Soil (S of Alltrades)
8: Mushroom
6: Grass
5: Sea
4: Flower
3: Sand, Ore, Water, Stone

Brighten Rock (NE of Gleeba)
8: Water
6: Stone
5: Ore
4: Sand
3: Grass, Sea, Flower, Mushroom

There is a list of every spawn point on gkwiki although most of them are fixed (for example, Coagulant outside Stornway is always 3)


More information from yab:
So in the main game, each of the 8 items has an equal (1/8) chance of appearing.
In post-game, each of the 14 items has a 1/16 chance, except for special items #1 and #2, which have a 1/8 chance of appearing.

What you get specifically is determined by the Hoimi table, so you can exploit it if you want:

Before completing:
00.00-12.49%: Medicinal herb
12.50-24.99%: Angel bell
25.00-37.49%: Emerald moss
37.50-49.99%: Holy water
50.00-62.49%: Special item #3
62.50-74.99%: Special item #1
75.00-82.49%: Special item #2
82.50-99.99%: Special item #4

00.00-06.24% Medicinal herb
06.25-12.49% Angel bell
12.50-18.74% Emerald moss
18.75-24.99% Holy water
25.00-31.24% Special item #3
31.25-37.49% Special item #1
37.50-43.74% Special item #2
43.75-49.99% Special item #4
50.00-56.24% Mini medal
56.25-62.49% Narspicious
62.50-68.74% Resurrock
68.75-74.99% Astral plume
75.00-81.24% Special item #1
81.25-87.49% Special item #2
87.50-93.74% Special item #5
93.75-99.99% Special item #6

For numbering purposes the items are arranged like this:

Grass group: Flurry feather, Ice crystal, Superior medicine, Softwort, Thinkincense, Yggdrasil leaf
Stone group: Ice crystal, Flurry feather, Rockbomb shard, Corundrum, Flintstone, Mirrorstone
Sea group: Evencloth, Lava lump, Seashell, Crimson coral, Mystifying mixture, Panacea
Ore group: Lava lump, Evencloth, Iron nails, Iron ore, Platinum ore, Mythril ore
Sand group: Royal soil, Brighten rock, Kitty litter, Glass frit, Malicite, Saint's ashes
Flower group: Brighten rock, Royal soil, Sleeping hibiscus, Nectar, Lunaria, Enchanted stone
Water group: Thunderball, Fresh water, Wakerobin, Nectar, Magic water, Sage's elixir
Mushroom group: Fresh water, Thunderball, Belle cap, Fisticup, Finessence, Aggressence