Here are the definitions of 'tūmahi whiti' (transitive verb) and 'tūmahi poro' (intransitive verb) from Te Aka
tūmahi whiti
1. transitive verb - a verb able to take a direct object.
tūmahi poro
1. intransitive verb - a verb not able to take a direct object.
I have added the bold bits.
In this context, ‘take’ just means ‘be followed by’.
These are great definitions.
Let's look at the verb 'kai' (to eat).
We can say:
E kai ana au
I am eating
This makes perfect sense, but is the verb 'kai' a transitive or intransitive verb?
Let's add an object:
E kai ana au i te hanawiti
I am eating the sandwich
The object (hanawiti) is getting 'verbed'; 'hanawiti' is a direct object.
So, the verb 'kai' is able to take a direct object; it is a transitive verb.
We can be sure that the 'i' before the object noun and its determiner ('te hanawiti') is correct.
How about the verb 'moe' (to sleep)?
E moe ana a Wiremu
Wiremu is sleeping
Can ‘moe’ take a direct object? I don’t think so, I can’t think of any sentence that would make sense if it said ‘Wiremu is sleeping something’
He could be sleeping in, on or under something, but the something is not a direct object.
Moe is unable to take a direct object and therefore it is an intransitive verb.