I think teaching fellowships can be extremely exploitative of young academics: often they're not fulltime in regards to salary, but demand practically fulltime commitment in terms of preparation, pastoral duties, etc. The piece-work nature of them and the emerging practice of paying just per course is bad news for young academics, not to mention that they're often only for a year or two and so require constant mobility. Holders of such posts often don't qualify for any of the additional perks and benefits that fulltime permanent staff enjoy, such as research expenses or even help with moving costs, which makes them even more exploitative. The problem is that there are so many people who want to remain in academia, and so few jobs, that people will apply for these positions just to keep their foot in the door in the hope of eventually gaining a permanent post.
Of course, there are some teaching positions which are fairly paid and demand a reasonable level of work in relation to the salary offered, but these seem to be less common than the barefaced cost-saving exercises that many teaching posts represent.
In terms of the experience required, the great majority of applicants that I know or have heard of going for these types of jobs will already have their PhD, or will be very close to completion. I have heard of some people applying for one-year, poorly-paid positions even with several years of postdoctoral experience under their belt. Of course, who is shortlisted for the job (and ultimately gets it) will reflect the interests and personal preferences (and often contacts) of the people on the selection committee, so sometimes people with relatively little experience, or even someone without a completed doctorate will be interviewed because of a connection with someone on the interview panel. I think these posts are supposedly designed with those who have just finished a PhD, or are close to completion, in mind as a way to gain experience. In practice, many of those applying even for short-term work will have a PhD and sometimes-extensive experience, due to the nature of the jobs market, and so the 'level' required to get one often goes up & up.