For Alphonse Mucha, being a "Modernist" in the 19th and 20th centuries was never as important as being in the right place at the right time: which is why for critics the Impressionists of the late 19th century are Modernist and Mucha, their contemporary, was merely modern.
By capital "M" Modernism I mean the singularity of mind that came to reject specific subject matter, was attentive to the "flatness" of the painting medium, and focused on the ideal of a pure art rather than an applied one. It was founded in a series of movements beginning with Impressionism and leading to Cubism and Orphism before ending with late 20th-century Abstract-Expressionism and Minimalism.
Alternately, in lowercase "m" modernity, artists respond directly to the present state of their own culture. The 19th-century French poet Charles Baudelaire said it best when his celebration of cultural "now-ness" led him to praise "the ephemeral, the fugitive, the contingent, the sketch of manners, the depiction of bourgeois life, the pageant of fashion; the pleasure we derive from the representation of the present is due to its essential quality of being present."