You can pour the oil on adjacent squares.
This is not spelled out very clearly, but your reach is assumed to be 5 feet unless specified otherwise. In the section on melee attacks, it is stated:
Most creatures have a 5-foot reach and can thus attack targets within 5 feet of them when making a melee attack. Certain creatures (typically those larger than Medium) have melee attacks with a greater reach than 5 feet, as noted in their descriptions.
Again, this is in the section on melee attacks, which may not appear to be entirely relevant. But the next paragraph has further guidance, concerning unarmed strikes:
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons).
So while it nowhere says I can pour my oil on an adjacent square, I can headbutt or punch enemies in adjacent squares, so it is quite natural that I can also pour a flask of oil into an adjacent square.