How did Haman, Corvil and Erith show up at the manor in Tear?

 

Were they heading back to Stedding Shangtai, pissed that they Loial in the Two Rivers, 5 books ago, and just decided to stop at every manor in the hopes they came across their wayward Ogier. 

 

Is Elder Haman Ta'Veren, to just show up att he right place at the right time? 

 

Is Erith, like my ex wife, possessed of some unearthly sixth or possible seventh, sense that allows her to know where Loial is and what he is doing at all times?

 

Or, was it Rand, as ta'veren, drawing to him what he needs, which is assistance from the Ogier, which he reluctantly gets from Elder Haman? 

 

Rand, I think. Perrin can feel Rand pulling at him when Perrins just saved the Two Rivers

The latter seems the most likely.

It was Rand. Loial needed rest and could not help any longer

Loial could probably have helped Rand some more. But by sending Loial to the stedding, there is a great chance the ogier will stay and fight instead of leaving, and ogier is definitly a force you want by your side.