There is no activity parsing for unknown assets. They're just treated like every day posts. It's not possible for it to be able to parse out activity for a page it doesn't know anything about. You need to implement display parsing in the core activity template page or just let it act like a normal activity post by supplying a Title and/or Message when creating the activity in CB Auto Actions.

The below for example should create an activity entry, but it has no display parsing of any kind so it's just going to look like a profile post.

Global
Triggers: activity_onAfterLikeStream
Type: CB Activity
User: Automatic
Access: Everybody
Conditions
1: [var3_asset] Is REGEXP /^hotspot./
Action
Mode: Activity
Method: Create
Asset: [var3_asset]
Owner: [var3_user_id]
Title: liked HOTSPOT
Date: [var3_date]
Load By: By Asset and Owner

This won't display on any activity stream unless that activity stream is setup to output the "hotspot.%" wildcard asset, "all" for all activity output, or is on a profile stream.

Do you have some special tags for this that I could add to the hotspot template ?

All activity is passed through the core activity template file. You can add your own custom display code there. Specifically the below file.

/components/com_comprofiler/plugin/user/plug_cbactivity/templates/default/activity_core.php

Do not modify the default. Make a new folder in the templates folder then copy activity_core.php to it. Next within CB Activity select your template. Now you can begin adding changes to it.

When I rewrite the template files this will change. My plan is to add automated parsing for activity template files that can just be dropped in. So you'd have something like the below instead.

/components/com_comprofiler/plugin/user/plug_cbactivity/templates/default/activity/login.php

In your case you'd just have the below.

/components/com_comprofiler/plugin/user/plug_cbactivity/templates/default/activity/hotspot.php

Note this functionality doesn't exist yet, but is the plan.

Knowing that each hotspot has already an activity on save, would it be possible to retrieve this activity data and display it in the second one ? media and links for instance

Where an activity displays on a stream is entirely dependent on the asset the stream outputs. Add hotspot.% and the stream should always display all activity entries with that asset.

We will wait for this functionality before implementing our template

That might be awhile. The activity_core.php will be sufficient for putting your custom activity display parsing. activity_core.php can handle access, display, and source parsing so it's a complete solution for custom activity display and access.

Is it possible to retrieve data related to hotspot.% in the CB activity like auto action that I prepared as above ? is this a var ?

No, CB Activity does not store source object data (it likely will store a serialized object in the future). It's parsed out from the asset. You can add custom parsing for that as well in activity_core.php in the parseSource function.