Filtering the feature service works on geographic extent. When you add the service you can filter by an area, your current view etc.
You can also modify the geographic extent after adding a feature service using the Set Geographic Extent button on the feature tab of the ribbon.
You cannot filter by attribute at this time. Clever use of subtypes or definition queries in your published maps can help you with data that needs to be “always” filtered in a certain way. If you use a definition query in your ArcMap layer and then publish that layer you will only be serving out data that conforms to that definition query. You have to be careful because adding data to that feature service may have attributes that don’t fit that query definition. They will be added to the underlying geodatabase but would be filtered out when feature’s are supplied back to the drawing.
This is the same type of experience you see when you draw features outside the spatial limits of a feature service. You an add the feature but when you refresh the drawing only the features within the spatial limits will be returned to you, because that is what you asked for.