For a start you need to clean all the sap which is gradually crystallizing on the top of the affected wood.
Attic wood leaking sap.
While there are complex chemical components found in tree sap it s easy to compare sap to blood.
Use a coarse plastic sponge to scrape the oozed resinous compounds and go over the surface of the wood with a clean towel.
Sap is just sugar and water.
Just use a razor bladed scraper remove off the timber and let it be.
Hopefully not on your hands as you steady your walk through the attic.
You can try removing sap with several different cleaning techniques but there is a chance it will come back.
When it dries it hardens and becomes difficult to remove creating unsightly spots or bumps in the wood surface.
Treat the knot areas with extra coats of the finishing material.
Amber or rosin is great if you save it and use it for stuff like stickum on tools etc.
Turpentine works perfect for this purpose and it will not damage the quality of the wood.
Like kevin said the attic heat restores this to a liquid form and it flows out.
It probably got hot enough in the attic and it melted out this happens over time through many heating and cooling cycles.
Usually if the wood is properly kiln dried it bakes away.
The sap when in live trees carries nutrients throughout the tree that helps to keep it alive.
Much of the wood produced for framing lumber has pitch pockets or areas of crystalized resin.
These materials slow the leakage by clogging the wood grain pores but will not stop it completely.
Attic ambering refers to wooden beams in the attic having sap leak out.
Sap can caused a problem on decks and in houses where wood beams are used for support.
When it is wet it is sticky and can rub off on clothing or attract dust and dirt.
Similarly when a tree is damaged the sap can bleed out.