You can bake object transformation into keyframes using Set Keyframes node. It should work.

If you don't want to bake animation then try this method:

Step 1: Create empty objects using Object Instancer and do whatever animations you want to those empty objects.

Step 2: Create instances of actual object having particles using Object Instancer. Then unlink it from node. You can do that by pressing Unlink Instances From Node. which can be found on advanced settings of Object Instancer node.

Step 3. Set empties as parent for these objects using Attribute Output node.

You can bake object transformation into keyframes using Set Keyframes node. It should work.

If you don't want to bake animation then try this method:

Step 1: Create empty objects using Object Instancer and do whatever animations you want to those empty objects.

Step 2: Create instances of actual object having particles using Object Instancer. Then unlink it from node. You can do that by pressing Unlink Instances From Node. which can be found on advanced settings of Object Instancer node. Then move those objects into another collection.

Step 3. Get objects from collection using Collection Info node. Then set empties as parent for these objects using Attribute Output node.