Yes, talking about nappies a lot probably has effects on other aspects of one's internet usage. With massive data, google may well pick up these statistical trends.
A similar performance to a perceptive fortune teller. Google can appear to be a mind reader.
Apparently, walmart used to send targetted ads when the pattern for pregnancy was detected - which created problems where not all parties knew about it, so walmart disabled it.
Another commentor's two week experiment might need to have you think about nappies for the first "control" week, to account for this bias.
Also, note that "nappies" wasn't randomly selected, but suggested by the group. This choice and the ads may have had a common cause. e.g, Young adults concerned about pregnancy.