My DVR recordings were gone

If you replaced a DVR that stored recordings on a local hard drive, there's no way you could have retained those recordings, regardless of the type of new DVR you received.  The recordings were only available while using that particular DVR.  When it failed, your recordings were lost forever.  If it had been Cloud DVR, the recordings would (should) have been available when you got a new, replacement Cloud DVR.  The technician could have thought that was what you had, but he probably just lied to you. 

There have been numerous reported performance issues with Cloud DVR.  So, if you experience audio cut out, picture freeze, difficulty with fast forward, etc., it's not just you.

Here's a breakdown of the Cox Cloud DVR storage limits and features: (AI Overview)

• Starter DVR: Records one show at a time and stores up to 50 hours of HD video.
• Essential DVR: Records up to two shows at a time and stores up to 250 hours of HD video.
• Preferred DVR: Records up to six shows at a time and stores up to 250 hours of HD video.
• Ultimate DVR: Records up to 24 shows at a time and stores up to 1,000 hours of HD video.
• Cloud DVR Recordings: Recordings kept maximum one year, even if "Until space is needed" selected.
• Downloading Recordings: You can download recordings to your mobile devices and watch offline.
• Download Restrictions: Up to 50 titles downloaded to a device, using your Cox in-home Internet. 
• Simultaneous Viewing: Recordings cannot be viewed on more than one device at the same time. 

Since you didn't know you would have Cloud DVR, you may not know what package you have.  You probably have the Cloud DVR equivalent of what you had before, but you should verify that with Cox.