Here is what I get with showmanualtags
\listfiles
\documentclass{article}
\usepackage[overload, ntheorem]{empheq}
\mathtoolsset{showonlyrefs,showmanualtags}
\usepackage[amsmath]{ntheorem}
\usetagform{default}
\begin{document}
\begin{equation}
\tag{atag}
a.
\end{equation}
\begin{equation}
\label{eq}
b.
\end{equation}
See \refeq{eq}.
\end{document}

Using the following file versions:
*File List*
article.cls 2014/09/29 v1.4h Standard LaTeX document class
size10.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
empheq.sty 2017/03/31 v2.15 Emphasizing equations
mhsetup.sty 2017/03/31 v1.3 programming setup (MH)
mathtools.sty 2018/01/08 v1.21 mathematical typesetting tools
keyval.sty 2014/10/28 v1.15 key=value parser (DPC)
calc.sty 2017/05/25 v4.3 Infix arithmetic (KKT,FJ)
amsmath.sty 2017/09/02 v2.17a AMS math features
amstext.sty 2000/06/29 v2.01 AMS text
amsgen.sty 1999/11/30 v2.0 generic functions
amsbsy.sty 1999/11/29 v1.2d Bold Symbols
amsopn.sty 2016/03/08 v2.02 operator names
ntheorem.sty 2011/08/15 1.33
ifthen.sty 2014/09/29 v1.1c Standard LaTeX ifthen package (DPC)
graphicx.sty 2017/06/01 v1.1a Enhanced LaTeX Graphics (DPC,SPQR)
graphics.sty 2017/06/25 v1.2c Standard LaTeX Graphics (DPC,SPQR)
trig.sty 2016/01/03 v1.10 sin cos tan (DPC)
graphics.cfg 2016/06/04 v1.11 sample graphics configuration
pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex
supp-pdf.mkii
epstopdf-base.sty 2016/05/15 v2.6 Base part for package epstopdf
infwarerr.sty 2016/05/16 v1.4 Providing info/warning/error messages (HO)
grfext.sty 2016/05/16 v1.2 Manage graphics extensions (HO)
kvdefinekeys.sty 2016/05/16 v1.4 Define keys (HO)
ltxcmds.sty 2016/05/16 v1.23 LaTeX kernel commands for general use (HO)
kvoptions.sty 2016/05/16 v3.12 Key value format for package options (HO)
kvsetkeys.sty 2016/05/16 v1.17 Key value parser (HO)
etexcmds.sty 2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO)
ifluatex.sty 2016/05/16 v1.4 Provides the ifluatex switch (HO)
pdftexcmds.sty 2018/09/10 v0.29 Utility functions of pdfTeX for LuaTeX (HO)
ifpdf.sty 2018/09/07 v3.3 Provides the ifpdf switch
epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
***********
\tagI assume you want those printed always, remembershowmanualtagsfor the mathtools options. – daleif Nov 14 '18 at 12:21showmanualtagsdoes not solve the problem, the text is stillSee .with a missing reference to the second equation. (Indeed I usually useshowmanualtagsbut here I removed it to simplify the example as much as possible.) – Olivier Cailloux Nov 14 '18 at 16:38