You see, when Tyrion was set to lead the van (and I presume this means vanguard), he found himself on the _left_. But isn't the vanguard the _foremost_ units of an army?
Usage varied... but most often, the vanguard or van was the foremost division (or "battle," as they were called) of a medieval army in the =line of march.= However, when the army actually deployed for battle, the van would generally be on the left.
There are enough exceptions to this to make the issue confusing. Sometimes the van would be placed on the right rather than the left. If the host was attacking, the van would sometimes indeed be the shock unit, the first to smash into the enemy... but when the army was drawn up in a defenseive array, that obviously did not apply. It also depended somewhat on the size of the army and how it was organized; i.e. how many "battles" or divisions.