Trigger Event After Node Is Indexed
Both Solr modules provide APIs:


Apache Solr Search
Search API Solr


But neither provide an after-node-update hook. If I had to guess I'd say it's both modules send data to Solr in batches, not one node at a time.

You might get some joy with the core hook_node_update_index():


  Act on a node being indexed for searching.
  
  This hook is invoked during search indexing, after node_load(), and after the result of node_view() is added as $node->rendered to the node object.