To my Knowledge, you should not get assigned monsters that require you to do a quest, without doing the quest first. few examples
you will not get assigned mogers, untill you do the miniquest for it.
you should not get assigned zygomites unless you complete lost city
you will not get assigned jungle beast or cave beast without completing cabin fever.
my alternate account keeps getting assigned stuff from the lost city quest. the slayer master should not give me a monster i cannot reach. i have never experienced this in my entire runescape life of 12 years or so.