npm run tests in docker with travis CI - reactjs

Question

I am deploying a react app to Heroku via TravisCI. The fact that I'm using Heroku doesn't really affect what I'm about to ask, I'm pretty sure, it's just there for context. Travis successfully deploys the app until I add a testing step (the script section) in .travis.yml:
language: generic
sudo: required
services:
- docker
before_install:
- docker build -t myapp:prod -f Dockerfile.prod .
script:
- docker run -e CI=true myapp:prod npm run test
after_success:
- docker build -t myapp:prod -f Dockerfile.prod .
- echo "$DOCKER_PASSWORD" | docker login -u "$DOCKER_ID" --password-stdin
- docker push myapp:prod
deploy:
provider: heroku
app: myapp
skip_cleanup: true
api_key:
secure: <my_key>
However, my Dockerfile.prod is a multi-stage node + nginx where the nginx stage doesn't keep any node or npm stuff:
# build environment
FROM node:13.12.0-alpine as builder
# set working directory
WORKDIR /app
# add `/app/node_modules/.bin` to $PATH
ENV PATH /app/node_modules/.bin:$PATH
# install app dependencies
COPY package.json ./
COPY package-lock.json ./
# some CI stuff I guess
RUN npm ci
RUN npm install react-scripts#3.4.1 -g --silent
COPY . ./
RUN npm run build
# production environment
FROM nginx:stable-alpine
COPY nginx.conf /etc/nginx/conf.d/default.conf
# If using React Router
COPY --from=builder /app/build /usr/share/nginx/html
# For Heroku
CMD sed -i -e 's/$PORT/'"$PORT"'/g' /etc/nginx/conf.d/default.conf && nginx -g 'daemon off;'
Therefore, it is my understanding that .travis.yml tries to run that npm run test command inside my nginx container and can't execute npm commands (no node installed, right?). So guided by SO answers such as this one I started adding commands into that nginx stage such as
COPY package.json ./
COPY package-lock.json ./
RUN apk add --update npm
but I realized I might be approaching this the wrong way. Should I perhaps be adding npm through Travis? That is, should I include in .travis.yml in the scripts section something like docker run -e CI=true myapp:prod apk add --update npm and whatever else is necessary? This would result in a smaller nginx image no? However, would I run into problems with package.json from the node stage in Dockerfile.prod or anything like that?
In summary, to use TravisCI to test a dockerized react app served with nginx, at what point should I install npm into my image? Does it happen as part of script in .travis.yml or does it happen in Dockerfile.prod? If it is recommened to npm run tests inside Dockerfile.prod, would I do that in the first stage (node) or the second (nginx)?
Thanks
EDIT: Not sure if this can be considered solved, but a user on Reddit recommended to simply RUN npm run test right before the RUN npm run build.