If a line of machines are requesting stacks of items, the transporters will only ever check the first target and, as such, not pull nearly enough items to fulfil the line.

You have to use the sorter if you wish for it to "round robin" hope this helps

It's not round-robin, but more so that the transporters will never pull to their proper specification, if the first-most destination only allows 1 item then the transporters will only ever transport 1 item at a time. Similarly if the source inventory's last-most slot only has 1 item then the transporters will only ever pull that one item until the slot moves or you use a secondary transporter on the same inventory.

And if you think this may be by design to prevent over-pulling, it definitely isn't because the transporters will over-pull regardless of the source and destination conditions (unless all the destinations are completely full), often resulting in single-item stacks bouncing back and forth in the transporters.

Also, in the current release I'm using, the sorter is basically non-functional so I cant use it anyway...
(#4214)

are pipes connecting destination machines colored? can you show a screenshot?

Colours are not used, it's just single lines of transporters pulling from a chest each (1 source, 16 destinations).

Cant show screenshots currently as the transporters were stripped out once I discovered the bug.

This is to avoid inefficiency; only one destination is considered per calculation. As mentioned previously, use round robin mode if you want to distribute destinations.