This is actually a case of badly labeled tabs, what they do and what we assume they do are 2 totally different things.
In Sales > Customers > Customers (left nav bar in admin) : this section deals exclusively with just the customers account, it doesn't actually relate to past order details. When you click on a customer (edit pencil) it brings up the following tabs: General, History, transactions, reward points, IP Addresses. Here's what these tabs actually do (rather than what we assume they do!)
General - customer details etc
History - this section is not the order history, rather it is a place to add an internal comment to do with the actual customer. Such as "Make sure you plastic pack this one as last time the postman left it in the dog bowl around the back of the house!" etc. this is purely for internal comments on the customer themselves.
Transactions - This is terribly named! This is actually a section to add credit to a customers account. So for example say you wanted to give a customer a direct discount for whatever reason, you would put a little description as to why, and then whatever amount you would like to add to that customers account. So for example "Last order took awhile to get delivered, so here's £2.75 to cover the postage of your next order". This will then be discounted from the customers next purchase.
Reward points - Same as the the transactions section but for the reward points system.
IP Addresses - This is a log of IP's the customer has used, I think!
So a little different to what we assume! If you want so see an overview of how much a particular customer has spent etc, go to Reports > Customers > Orders this will tell you how many orders they have made, the number of products in total, and their total spend.
Now, should you want to see all the orders a customer has made, go to Sales > Orders and in the grey box at the top put in the customers name and click the blue "filter" button. This will bring up all of the processed orders for that particular customer. These cannot be displayed inline with all of the order details as it would be a MASSIVE strain on the database pulling that many variables onto one page. Each order is split over five tabs in itself, and each order pulls a minimum of 37 data sets from the database (even more for each product ordered and history added (such as pending, shipped etc") on that particular order). So as you can imagine if you have a particularity prolific customer that has made say 10 orders, that's a minimum of 370 data requests from the database... Which is massive to say the least! Hence why you have to go into the actual order to display it's variables and on the main orders page you get a brief overview. Makes sense really! Just saves from overloading they system and causing it to crash/restart.
Hope this helps