It seems (not 100% this is the real root cause) that if there is no 'trunk' or 'branches' structure in the SVN checkout, the multibranch pipeline does not find the Jenkinsfiles.

The SVN structure is as follows:
svn/apps/project_name/trunk
svn/apps/project_name/branches/...

My original setup works fine:
project_name/trunk/jenkins/instances/branch_A/Jenkinsfile
project_name/trunk/jenkins/instances/branch_B/Jenkinsfile

I point to the project/name/jenkins/instances folder and include all branches, and the jobs are properly launched.

However, when I moved everything in the following manner:
svn/apps/jenkins/instances/branch_A/Jenkinsfile
svn/apps/jenkins/instances/branch_B/Jenkinsfile

when targetting jenkins/instances/ (include all branches), the branches are found, but I get the following message at scan time:
Checking candidate branch /jenkins/instances/op-br-3dxp-2017x@17597
‘Jenkinsfile’ not found

Environment dump (sorry, not user friendly at all)

ace-editor 1.1 true
active-directory 2.0 true
analysis-core 1.82 true
ant 1.4 true
antisamy-markup-formatter 1.5 true
authentication-tokens 1.3 true
authorize-project 1.3.0 true
bouncycastle-api 2.16.0 true
branch-api 2.0.6 true
build-flow-plugin 0.20 true
build-monitor-plugin 1.11+build.201701152243 true
build-pipeline-plugin 1.5.6 true
build-timeout 1.18 true
buildgraph-view 1.5 true
cloudbees-folder 5.17 true
conditional-buildstep 1.3.5 true
config-file-provider 2.15.6 true
credentials 2.1.11 true
credentials-binding 1.10 true
cvs 2.13 true
delivery-pipeline-plugin 0.10.2 true
dependencyanalyzer 0.7 true
depgraph-view 0.11 true
description-setter 1.10 true
display-url-api 1.1.1 true
docker-commons 1.6 true
docker-workflow 1.10 true
durable-task 1.13 true
email-ext 2.56 true
emailext-template 1.0 true
envinject 1.93.1 true
exaplugin 1.0.1 true
extended-choice-parameter 0.75 true
external-monitor-job 1.7 true
findbugs 4.69 true
fstrigger 0.39 true
git 3.0.5 true
git-client 2.2.1 true
git-server 1.7 true
github 1.26.0 true
github-api 1.84 true
github-branch-source 2.0.3 true
github-organization-folder 1.6 true
gradle 1.26 true
greenballs 1.15 true
handlebars 1.1.1 true
hudson-wsclean-plugin 1.0.5 true
icon-shim 2.0.3 true
instant-messaging 1.35 true
ivy 1.27.1 true
jabber 1.35 true
jacoco 2.1.0 true
javadoc 1.4 true
job-dsl 1.57 true
jobConfigHistory 2.15 true
jquery 1.11.2-0 true
jquery-detached 1.2.1 true
jquery-ui 1.0.2 true
junit 1.20 true
ldap 1.14 true
m2-repo-reaper 1.0 true
m2release 0.14.0 true
mailer 1.19 true
mapdb-api 1.0.9.0 true
matrix-auth 1.4 true
matrix-project 1.8 true
maven-invoker-plugin 1.2 true
maven-plugin 2.14 true
maven-release-cascade 1.3.2 true
maven-repo-cleaner 1.2 true
momentjs 1.1.1 true
monitoring 1.63.0 true
nexus-artifact-uploader 2.9 true
nodejs 0.2.2 true
nodelabelparameter 1.7.2 true
openJDK-native-plugin 1.1 true
pam-auth 1.3 true
parameterized-trigger 2.32 true
performance 2.0 true
pipeline-build-step 2.4 true
pipeline-github-lib 1.0 true
pipeline-graph-analysis 1.3 true
pipeline-input-step 2.5 true
pipeline-milestone-step 1.3 true
pipeline-model-api 1.0.1 true
pipeline-model-declarative-agent 1.0.1 true
pipeline-model-definition 1.0.1 true
pipeline-rest-api 2.5 true
pipeline-stage-step 2.2 true
pipeline-stage-tags-metadata 1.0.1 true
pipeline-stage-view 2.5 true
pipeline-utility-steps 1.2.2 true
plain-credentials 1.4 true
powershell 1.3 true
promoted-builds 2.28.1 true
queue-cleanup 1.0 true
rebuild 1.25 true
resource-disposer 0.6 true
ruby-runtime 0.13 true
run-condition 1.0 true
saferestart 0.3 true
scm-api 2.0.4 true
scm-sync-configuration 0.0.10 true
script-security 1.26 true
seed 2.1.4 true
simple-build-for-pipeline 0.2 true
simple-travis-runner 1.0 true
ssh-agent 1.14 true
ssh-credentials 1.13 true
ssh-slaves 1.13 true
structs 1.6 true
subversion 2.7.1 true
timestamper 1.8.8 true
token-macro 2.0 true
toolenv 1.1 true
travis-yml 0.2.2 true
windows-slaves 1.2 true
workflow-aggregator 2.5 true
workflow-api 2.11 true
workflow-basic-steps 2.4 true
workflow-cps 2.27 true
workflow-cps-global-lib 2.6 true
workflow-durable-task-step 2.9 true
workflow-job 2.10 true
workflow-multibranch 2.12 true
workflow-remote-loader 1.4 true
workflow-scm-step 2.3 true
workflow-step-api 2.9 true
workflow-support 2.13 true
ws-cleanup 0.32 true