At your discretion a partial dose of poison may have (reduced) effects.
The DMG (257-258) distinguishes between different kinds of poisons and how they take effect, by contact, inhaled, by injury or Ingested (DMG 257):
Ingested. A creature must swallow an entire dose of ingested poison to suffer its effects. You might decide that a partial dose has a reduced effect, such as allowing advantage on the saving throw or dealing only half damage on a failed save.
Handle it at your discretion. Maybe you want to use the Variant rule on the same page (DMG 136) that makes identification generally more difficult and adjust it by making it explicit that tasting potions is dangerous or bears no effect at all.
The narration of poisons are mostly at your discretion as well, you define whether they are tasteless, smell-less, indistinguishable (for that matter you also narrate the smell and taste of magic potions and you may indulge in that healing potions taste foul or like soap), etc. How identifying potions should work gives narrative techniques.
Contact poison only works on exposed skin by RAW, but as a DM you are free to change that (you should inform your players when you do that and before it has negative consequences for them) your character's lips and mouth technically is all mucous membranes and not skin. But I'm not arguing that point, if you think it is skin, then contact poison affects you while tasting. These mucous membranes of humans are even thinner than skin and in that way, realistically speaking, may be affected by contact poison (DMG 257):
Contact. A creature that touches contact poison with
exposed skin suffers its effects.
The uncommon magic item (potion) Potion of Poison, (DMG 188):
This concoction looks, smells, and tastes like a potion of healing
or other beneficial potion. However, it is actually poison masked by
illusion magic. An identify spell reveals its true nature.
tastes like the mimicked potion by illusion magic, that is it tastes like whatever potion it is masked as (which you can narrate as you like). Which is contrary to its true nature - revealed by an identify spell. So the actual taste is not that of the mimicked potion (which you can narrate as you like).
The tasting of a Potion of Poison replicates the look and smells with illusion magic. It does not replicate the healing effect or other benevolent potion effects.