I think Royal Canadian Bandit nailed it in the comments. The expansion of the Culture's population is achieved through the influence and acceptance of other civilisations into it rather than making lots of babies. I'd venture further, however, and say that it is deliberate, or at least wilfully tolerated. Although Iain Banks does say in his notes that the Culture does not "actively encourage immigration", in the very next sentence he articulates the means of their expansion:
Contact's preferred methods are intended to help other civilisations
develop their own potential as a whole, and are designed to neither
leech away their best and brightest, nor turn such civilisations into
miniature versions of the Culture.
Since "potential" is from the perspective of the Culture, it is defined by Culture values. Therefore, Contact mentors other civilisations towards a future state that is morally in line with that of the culture itself, at which point it is indistinguishable and becomes a part of it by default. While its conscious aim is not to turn them into mini-Cultures, the end result is just that.
Flere-Imsaho in The Player of Games provides one of many examples of the purposeful influencing of a civilisation's path to one more closely aligned with the Cultire's values, implying careful consideration of the options to achieve the desired end-state (spoiler alert).
"The Empire's been ripe to fall for decades; it needed a big push, but
it could always go. Coming in 'all guns blazing' as you put it is
almost never the right approach; Azad - the game itself - had to be
discredited. It was what had held the Empire together all these years
- the linchpin; but that made it the most vulnerable point too."
As well as the means, Banks also discusses the Minds' and humans' benign motivations for meddling:
Interest - the delight in experience, in understanding - comes from
the unknown; understanding is a process as well as a state, denoting
the shift from the unknown to the known, from the random to the
The humans of the Culture, having solved all the obvious problems of
their shared pasts to be free from hunger, want, disease and the fear
of natural disaster and attack, would find it a slightly empty
existence only and merely enjoying themselves, and so need the
good-works of the Contact section to let them feel vicariously useful.
Guiding another race towards your own set of principles is morally ambiguous to say the least and the Culture is acutely aware of this. In Use of Weapons Sma sums this up nicely when justifying the existence of Special Circumstances:
“We think we’re right; we even think we can prove it, but we can never be sure; there are always arguments against us. There is no certainty; least of all in Special Circumstances, where the rules are different.”
This acknowledgement of the limits of their own knowledge supports the idea that they are doing it all out of curiosity. And as true scientists they appear open to the idea that other races could influence them in turn (rules being different), albeit through the concentric layers of SC, then Contact, then the civilisation as a whole. They and Iain Banks are perhaps a little embarrassed by the hypocrisy of their actions, but they can't help themselves.