An aggregate groups related business objects while an aggregate root (AR) is the 'representative' of that aggregate. Th AR itself is an entity modeling a (bigger, more complex) domain concept. In DDD a model is always relative to a context (the bounded context - BC) i.e that model is valid only in that BC.
This allows you to define a model representative of the specific business context and you don't need to shove everything in one model only. An Order is an AR in one context, while in another is just an id.
Since an AR pretty much encapsulates all the lower concepts and business rules, it acts as a whole i.e as a transaction/unit of work. A repository always works with AR because 1) a repo always deals with business objects and 2) the AR represents the business object for a given context.
When you have a use case involving 2 or more AR the business workflow and the correct modelling of that use case is paramount. In a lot of cases those AR can be modified independently (one doesn't care about other) or an AR changes as a result of other AR behaviour.
In your example, it's pretty trivial: when the customer places an order for 100 items, a domain event is generated and published. Then you have a handler which will check if the order complies with the customer promotions rules and if it does, a command is issued which will have the result of changing the client state to VIP.
Domain events are very powerful and allows you to implement transactions but in an eventual consistent environment. The old db transaction is an implementation detail and it's usually used when persisting one AR (remember AR are treated as a logical unit but persisting one may involve multiple tables hence db transaction).
Eventual consistency is a 'feature' of domain events which fits naturally a rich domain (and the real world actually). For some cases you might need instant consistency however those are particular cases and they are related to UI rather than how Domain works. Of course, it really depends from one domain to another. In your example, the customer won't mind it became a VIP 2 seconds or 2 minutes after the order was placed instead of the same milisecond.