Why is the ticks fontfamily not changing?

This is a hack that you can use until you get a better solution. Specify the tick labels yourself:

using Plots
pyplot()

x = 1:10
y = rand(10)
plot(x, y,
    guidefontsize = 12, tickfontsize = 10,
    xtick = (2:2:10, ["2", "4", "6", "8", "10"]),
    ytick = (0.2:0.2:1, ["0.2", "0.4", "0.6", "0.8", "1.0"]),
    xlabel = "x",
    ylabel = "y",
    fontfamily = "Times New Roman")

plot