I caught up with them. And I followed them means: I came in their tracks.
"Until, when drowning overtook him," the verse.
لَحِقْتُهُمْ، وَتَبِعْتُهُمْ: جِئْتُ فِي إِثْرِهِمْ.
﴿حَتَّى إِذا أدْركهُ الْغَرق﴾ الْآيَة