Associate a SharePoint 2010 workflow with my content type. it is not working

Question

I am a bit confused if I can have these working together:-

Inside SharePoint server 2013 and using sharepoint designer 2013, can I associate a SharePoint workflow-2010 with a Content type?

I have the following case, which I need to improve:-

1. I have a team site collection, which contain a site template. and i am creating sub-sites using this site template.
2. now inside the site template, i have many list workflows as follow:-
3. now when I create a new sub-site based on the template, the new sub-site will have the list workflow created which is fine.
4. but the limitation Ii am facing is that if we want to modify the workflow for all the lists. then I need to go to each sub-site and modify the related list workflow.

so I was thinking if I can associate the workflow with a site content type rather than associate with a list. so if I want to modify the workflow, iI will modify it from the content type level and have the effect on all the associated list content type and lists.

so i did the following as a test:-

1. i open sharepoint designer 2013.
2. i create a new sharepoint 2010 reusable workflow.
3. save it , then publish it.
4. i went to a content type inside sharepoint designer. click on "associate existing workflow", and i select the reusable workflow i just created:-

5. final step inside the site setting page, i set to update all the content type as follow:-

so now based on my understanding, i should have the following:-

1. a workflow associated with a site content type.
2. and this workflow should be associated with all the list content types (based on step 5).

but i am facing this problem:-

1. when i create/edit an item, the workflow will not work/fire.
2. also when i went to the related list content type and i checked the related workflows, i can not see the reusable workflow i just added.

so can anyone adivce on this please?

side note i have read some articles which mentioned that associating a workflow with a content type is not a valid option in SP2013 as mentioned on this link for example. although in SP designer the options are there.

so can anyone adivce on this please? how i can define a workflow at the content type level, so all the lists which uses this content type will have the workflow ,, is this possible ?