I am not a MAC guy, I started back in the day with IBM punch cards programming with them in COBOL,other codes, DOS back in the late 80s, Windows early 90's 3.1, 3.11 started programming in C++ OO etc 91 to 2001 over 20 apps and 67 games created. 2003 to mid 2010 Linux Network Media Players Coding, Then Android in 2010 I wrote ROMs for Android over 100 ROM and still going into 2014 doing the same. Over 40 tablets, 15 smartphones. Not even touch the surface with servers OS, and client OS. But no MAC. I've work with it but never own them.
Its good to learn from each other. Your issue is simple one since all I do is program in Android today but in hand I would with Windows and Android since both can be use today in what I do since 2010.
Do this, take the micro SD card or full SD card whichever tablet you have insert into your MAC if it your MAC doesn't support media card storage then get an USB 15-in-1 reader/writer. Since I don't do MAC you would have look into that. All my systems have that feature built in Windows system. Copy the files to a folder an Android that app will see them and run the media or what I do use NSA 325 from ZyXEL. That can hold up to 6 TB of storage. They have Android app for that NAS too.
Think of the NAS a another computer that doesn't have Monitor or keyboard or mouse. It's always on 24/7 but uses less energy since it so small Holds 2 HDD. Place that on the network that can hold your collection of videos. I record HDTV 1080i on my Windows 7 64-bit that but you need Windows system to play it back because of the format MS uses. I use laptops, netbooks, tablet and desktop to watch what has been recorded. Most are connect to the HDTV via HDMI. Then I use Logitech Harmony Remote and USB IR on Computer then you can control the PC with the TV.
That's how I do it on the Windows side. I am sure MAC as something like that for MAC PC side.