That is true, but I don't think there is much evidence for people imagining steam engines for doing useful work prior to Thomas Savery (update: Jerónimo de Ayanz y Beaumont appears to have preceded him by almost a century.) Admittedly, absence of evidence does not settle the issue, but AFAIK Leonardo never sketched one, even though he did propose a steam cannon. If he had conceived of a rotary steam engine, or the idea was 'in the air', how could he have resisted the appeal of a horseless carriage?

One technical point: Jerónimo's and Savery's pumps used pressurized steam, but Newcomen and Watt used it at atmospheric pressure. The latter, at least, was dead set against using pressurized steam on account of the risks it posed given the technology of the day (a well-founded concern, as it turned out.)