We prove higher order mean curvature estimates for properly immersed $$\phi _h$$ -bounded hypersurfaces $$M^m \rightarrow (N \times L)^{m+1}$$ . The class of $$\phi _h$$ -bounded submanifolds, introduced by Bessa et al. (Annali di Matematica Pura ed Applicata 194(1):109–130, 2015), contains properly the class of cylindrically bounded submanifolds. The estimates we prove here depend only on the geometry of N and L and extend previous results of Alias et al. (Nonlinear Anal 84:73–83, 2013), Bessa et al. (An Acad Bras Cien 78(3):391–404, 2006), Fontenele and Silva (Houst J Math 32:47–57, 2006), Ranjbar-Motlagh (Bol Soc Brasil Mat 32:159–171, 2001), Roth (Math Z 258:227–240, 2008), Veeravalli (Expo Math 20:255–261, 2002) and Vlachos (Geom Dedicata 68:73–78, 1997). We point out that our assumption on the geometry of N does not impose any lower curvature bounds. We also consider spacelike properly immersed $$\phi _h$$ -bounded hypersurfaces of $$N\times L$$ where N is a spacetime manifold and L is a Riemannian manifold. In this setting, we prove higher order mean curvature estimates extending results of Alias et al. (Nonlinear Anal 84:73–83, 2013) and Impera (J Geom Phys 62:412–426, 2012).