[Bugfix][Mamba] Fix Multistep on Mamba-like models (#10705)

Signed-off-by: mzusman <mor.zusmann@gmail.com>

vllm/engine/async_llm_engine.py

@@ -300,6 +300,9 @@ class _AsyncLLMEngine(LLMEngine):
             ctx.seq_group_metadata_list = seq_group_metadata_list
             ctx.scheduler_outputs = scheduler_outputs
 
+            finished_requests_ids = self.scheduler[
+                virtual_engine].get_and_reset_finished_requests_ids()
+
             # Maybe switch from async mode to sync mode
             if not allow_async_output_proc and len(ctx.output_queue) > 0:
                 self._process_model_outputs(ctx=ctx)
@@ -311,13 +314,13 @@ class _AsyncLLMEngine(LLMEngine):
                 self._cache_scheduler_outputs_for_multi_step(
                     virtual_engine, seq_group_metadata_list, scheduler_outputs,
                     allow_async_output_proc)
+        else:
+            finished_requests_ids = list()
 
         assert seq_group_metadata_list is not None
         assert scheduler_outputs is not None
 
         if not scheduler_outputs.is_empty():
-            finished_requests_ids = self.scheduler[
-                virtual_engine].get_and_reset_finished_requests_ids()
 
             # Check if we have a cached last_output from the previous iteration.
             # For supporting PP this is probably the best way to pass the