target machine is the one in the office
If you are talking about host servers then you are really talking about terminal server/citrix.
From your initial post with questions like 'does someone have to be at the office PC ' I presumed you were talking about services like Jump.
Delays are caused by access moving data across the network to local memory and then acting on it and then (perhaps) 'putting it back'. Compare performance between a backend on your C drive v on the network. Simplistically, the reason it is faster on your C drive is because the 'journey' is much shorter and the pathways are much wider so more data can be transferred in a shorter period of time.
With remote access, no data is transferred to the mobile device, only an image of the screen - and it basically updates where things have changed - this is the same principle for optimising files sizes for video files. A 1 minute video of a screen where nothing moves will have a much smaller file size than one where the there is lots of movement/changes.
You can try Jump etc for free so suggest you try it and you'll perhaps understand better. You can also try the Access hosting you found (it is basically terminal server) - although $19 is only for a runtime version and it is not clear to me whether that is a price per application or price per user. And if your system is integrated with outlook, excel etc it is even more expensive.
What you
don't have is a front end on your pc and backend on the remote server.
This is not the same as a webpage where you enter data on your pc which is then transmitted to a server which then responds.
Note what it says
Our virtual desktop hosting easily allows multiple concurrent users to access the same database via any device (Windows, Macintosh, iPhone, iPad, Android, etc) from a web browser or using an RDP Connection. This is a full windows desktop machine rendered on any device that has the full functionality of Access 2010 in any HTML5 web browser.
I would expect that having front end and backend on the remote server, performance would actually be quicker since all the processing is done on the server and not on the pc.
What is not clear from their details is what type of server you have access to - in the same way a computer with slow drives and processors and little memory will be slower than a top of the range computer, the same is true of servers.
In summary, you need to investigate and decide what is right for you